tag:blogger.com,1999:blog-66441025958210103882024-02-19T07:29:16.644-08:00PHYSIC LESSONSΗ Βιβλιοθήκη της ΦYΣIKHΣ
ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comBlogger1072125tag:blogger.com,1999:blog-6644102595821010388.post-40945355509538640312021-10-20T13:30:00.000-07:002021-10-21T03:50:16.736-07:00ΑΡΧΙΚΗ<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: verdana;"><span face=""verdana" , sans-serif" style="color: red; font-size: x-large;"><b>ΑΡΧΙΚΗ</b></span><br />
<span face=""verdana" , sans-serif"><br /></span><span face=""verdana" , sans-serif"> <b>Καλώς ήρθατε στο <span style="color: blue;">PHYSIC LESSONS</span> τη <span style="color: red;">Βιβλιοθήκη της </span></b><b><span style="color: red;">ΦΥΣΙΚΗΣ</span></b><b>.</b></span><br />
<span face=""verdana" , sans-serif"><b> Στο ιστολόγιο αυτό περιέχονται <span style="color: #274e13;">ΘΕΜΑΤΑ ΦΥΣΙΚΗΣ</span>,</b></span><span face=""verdana" , sans-serif"><b>που απευθύνονται </b></span><b>σε σπουδαστές Τ.Ε.Ι.,φοιτητές Α.Ε.Ι.,</b><b>μαθητές Γυμνασίου και Λυκείου,αλλά και σε συναδέλφους Φυσικούς.</b><br />
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<span style="font-family: verdana;"><b><span face=""verdana" , sans-serif"> Το ιστολόγιο περιέχει </span><span face=""verdana" , sans-serif">Τομείς και Κλάδους της Φυσικής.</span><span face=""verdana" , sans-serif">Αναλυτική θεωρία,ασκήσεις και ερωτήσεις για όλες τις τάξεις του Γυμνασίου και Λυκείου.</span><span face=""verdana" , sans-serif">Λεξικό Φυσικής,Βραβείο Νόμπελ Φυσικής,Ιστορία της Φυσικής,Βιογραφία και έργο Φυσικών και Βιογραφία και έργο Αρχαίων Ελλήνων επιστημών.</span></b><br />
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<span style="font-family: verdana;"><span face=""verdana" , sans-serif" style="color: red; font-size: x-large;"><b>ΚΑΤΗΓΟΡΙΕΣ</b></span><br />
<span face=""verdana" , sans-serif" style="color: red;"><b><br /></b></span></span></div>
<span style="font-family: verdana;"><span style="font-size: x-small;"><span face=""verdana" , sans-serif"><b><a href="http://physiclessons.blogspot.gr/p/blog-page_25.html">ΛΕΞΙΚΟ ΦΥΣΙΚΗΣ</a></b></span></span><br />
<span style="font-size: x-small;"><span face=""verdana" , sans-serif"><br /></span></span><span face=""verdana" , sans-serif" style="color: red;"><b>ΓΥΜΝΑΣΙΟ</b></span><br />
<span face=""verdana" , sans-serif" style="color: red; font-size: x-small;"><b><br /></b></span>
<span face=""verdana" , sans-serif" style="color: red; font-size: x-small;"><b><a href="http://physiclessons.blogspot.gr/2014/12/blog-post_15.html">ΦΥΣΙΚΗ A ΓΥΜΝΑΣΙΟΥ</a></b></span><br />
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<span face=""verdana" , sans-serif" style="font-size: x-small;"><br /></span><span face=""verdana" , sans-serif" style="color: red;"><b>ΛΥΚΕΙΟ</b></span><br />
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<span face=""verdana" , sans-serif" style="color: red;"><b>ΕΝΔΙΑΦΕΡΟΝΤΑ</b></span><br />
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-15560038676332990122021-10-20T04:34:00.005-07:002022-01-27T10:54:21.477-08:00Exact mathematical Formula that connect 6 dimensionless physical constants <p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: georgia; font-size: large;">Exact mathematical Formula that connect 6 dimensionless physical constants </span></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: #666666; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Stergios Pellis </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><a href="mailto:sterpellis@gmail.com" style="text-decoration: none;"><span style="background-color: transparent; color: #666666; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">sterpellis@gmail.com</span></a></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><a href="http://physiclessons.blogspot.com/" style="text-decoration: none;"><span style="background-color: transparent; color: #666666; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">http://physiclessons.blogspot.com/</span></a><span style="background-color: transparent; color: #666666; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: white; color: #666666; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Department of Physics of the University of Ioannina</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: #666666; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> Greece </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span id="docs-internal-guid-80d8600f-7fff-3010-002c-c7c535958291"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: #666666; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">18 October 2021</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Abstract</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14.6667px; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b> </b></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">In this paper are a new formula for the Planck length </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">ℓ</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">pℓ and a new formula for the Avogadro number N</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. Also 9 Mathematical formulas that connect dimensionless physical constants. The 6 dimensionless physical constants are the Proton to Electron Mass Ratio μ,the Fine-structure constant α,the ratio Ν</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> of electric force to gravitational force between electron and proton,the Avogadro number N</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">,the Gravitational coupling constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> for the electron and the gravitational coupling constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G(p)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> of proton. After a new formula for Gravitational Constant G and new exact formula for the Avogadro number N</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. Finally 8 exact Mathematical formulas that connect 6 dimensionless physical constants and a new exact formula for Gravitational Constant G. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1. Introduction</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14.6667px; white-space: pre-wrap;"><b> </b></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; white-space: pre-wrap;">In physics,a dimensionless physical constant is a physical constant that is dimensionless,a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used. The term fundamental physical constant is used to refer to some universal dimensionless constants. A long-sought goal of theoretical physics is to find first principles from which all of the fundamental dimensionless constants can be calculated and compared to the measured values.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; white-space: pre-wrap;"> In the 1.920s and 1.930s,Arthur Eddington embarked upon extensive mathematical investigation into the relations between the fundamental quantities in basic physical theories,later used as part of his effort to construct an overarching theory unifying quantum mechanics and cosmological physics. The mathematician Simon Plouffe has made an extensive search of computer databases of mathematical formulas,seeking formulas for the mass ratios of the fundamental particles. An empirical relation between the masses of the electron,muon and tau has been discovered by physicist Yoshio Koide,but this formula remains unexplained. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2. Measurement of the 6 dimensionless physical constants </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2.1. Measurement of the Fine Structure constant</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; white-space: pre-wrap;"><b> </b>The 2.018 CODATA recommended value of α is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α=q</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/4</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ε</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ħ</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">c=0.0072973525693(11)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> With standard Uncertainty 0,0000000011×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3 </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and Relative Standard Uncertainty 1,5×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. For reasons of convenience,historically the value of the reciprocal of the fine-structure constant is often specified. The 2.018 CODATA recommended value is given by: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">= 137,035999084(21)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> With standard Uncertainty 0,000000021×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3 </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and Relative Standard Uncertainty 1,5×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. There is general agreement for the value of α,as measured by these different methods. The preferred methods in 2.019 are measurements of electron anomalous magnetic moments and of photon recoil in atom interferometry. The most precise value of α obtained experimentally (as of 2.012) is based on a measurement of g using a one-electron so-called "quantum cyclotron" apparatus,together with a calculation via the theory of QED that involved 12.672 tenth-order Feynman diagrams: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=137,035999174(35)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> This measurement of α has a relative standard uncertainty of 2,5×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. This value and uncertainty are about the same as the latest experimental results. Further refinement of this work were published by the end of 2.020,giving the value: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=137,035999206(11) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">with a relative accuracy of 81 parts per trillion. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2.2. Measurement of the Proton to Electron Mass Ratio </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The 2.018 CODATA recommended value of the Proton to Electron Mass Ratio μ is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ=1.836,15267343</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> With standard Uncertainty 0,00000011 and Relative Standard Uncertainty 6,0×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. The value of μ is known at about 0,1 parts per billion. The value of μ is a solution of the equation: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">3·μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">-5.508·μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">-841·μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">+10·μ-2.111=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The 2.018 CODATA recommended value of μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=me/mp=0,000544617021487 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> With standard Uncertainty 0,000000000000033 and Relative Standard Uncertainty 6,0×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2.3. Measurement of the Gravitational coupling constant α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> for the electron</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b> </b>In physics,the gravitational coupling constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is a constant that characterizes the gravitational pull between a given pair of elementary particles. For the electron pair this constant is denoted by α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. The choice of units of measurement,but only with the choice of particles. The gravitational coupling constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is a scaling ratio that can be used to compare similar unit values from different scaling systems (Planck scale,atomic scale,and cosmological scale). The gravitational coupling constant can be used for comparison of length,range and force values. The gravitational coupling constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is defined as: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=G</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/ħ</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">c</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> There is so far no known way to measure α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> directly. The value of the constant gravitational coupling α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is only known in four significant digits. The approximate value of the constant gravitational coupling α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">≃1,751809945728109×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-45</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 7.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2.4. Measurement of the Gravitational coupling constant α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> for the electron</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b> </b>The gravitational coupling constant for the proton is produced similar to the electron,but replaces the mass of electrons with the mass of the protons. The gravitational coupling constant of the proton α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G(p)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is defined as: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=G</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">p</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/ħ</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">c </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The approximate value of the constant gravitational coupling of the proton α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">≃5,906151273795571x10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-39</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 7.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2.5. Measurement of the ratio Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> of electric force to gravitational force between electron and proton</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b> </b>The enormous value of the ratio of electric force to gravitational force was first pointed out by Bergen Davis in 1.904. But Weyl and Eddington suggested that the number was about 10</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">40</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> and was related to cosmological quantities. The electric force F</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">c</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> between electron and proton</span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">is defined as: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">F</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">c</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=q</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">²/4</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ε</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">r² </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The gravitational force F</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">g</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> between electron and proton is defined as: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">F</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">g</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=G</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">p</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/r² </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=F</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">c</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/F</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">g</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=q</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/4</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ε</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">p</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=k</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·q</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/G</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">p</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=α·ħ</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">c/G</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">p</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The approximate value of the ratio Ν</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> of electric force to gravitational force between electron and proton is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">≃2,26866072471432x10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">39</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2.6. Measurement of Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12px; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b> </b></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The most accurate definition of the Avogadro number N</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> value involves the change in molecular quantities and,in particular,the change in the value of an elementary charge. The exact value of the Avogadro number N</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=6,02214076×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">23</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 7.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The value of the Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> can also be written in numerical expressions: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">≃2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">79</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=6,044629098×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">23</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=84.446.885</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=6,02214076×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">23</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 7.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">3. New Formulas </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">3.1. New Formula for the Planck length </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">pℓ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The Bohr radius α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> is defined as: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=ħ/α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">c </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The reduced Planck constant ħ is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ħ=α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">c </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ħ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">me</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">c</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(ħ∙G/c</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">)=α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">me</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙(</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">me</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/ħ∙c) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(ħ∙G/c</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">)=α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙(</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">me</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/ħ∙c) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">pℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So the new formula for the Planck length</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">pℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">pℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (1) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">3.2. New formula for the Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Jeff Yee in his paper «The Relationship of the Mole and Charge» [10],the mole and charge are related by deriving Avogadro’s number from three constants,the Bohr radius,the Planck length and Euler’s number. The Avogadro number N</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> can be calculated from the Planck length </span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">ℓ</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">pℓ</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">,the Bohr radius α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">0</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> and Euler's number e: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/2·e·</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">pℓ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/2·e·α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So the new Formula for the Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 8pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 8pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=(2·e·α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (2) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> ∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=1 (3) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">4. Mathematical Formulas that connects dimensionless physical constants </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">4.1. Mathematical Formulas that connects 3 dimensionless physical constants</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><b> </b>The exact mathematical formula that connects the mass ratio of proton to electron,the fine-structure constant α and the proton-proton gravitational coupling constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G(pp)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·[α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(pp)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·log</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(2·π)]</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The exact mathematical formula that connects the mass ratio of proton to electron,the fine-structure constant α and the proton-electron gravitational coupling constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G(pe)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·[α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(pp)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·log</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(2·π)]</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The exact mathematical formula that connects the mass ratio of proton to electron,the fine-structure constant α and the gravitational coupling constant of electrons-electrons α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G(ee)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·[α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(pp)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·log2(2·π)]</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The exact mathematical formula that connects the Proton to Electron Mass Ratio μ,the fine-structure constant α,the Gravitational coupling constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> for the electron and the gravitational coupling constant of proton α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G(p)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The mathematical formula that connects the Proton to Electron Mass Ratio μ,the ratio Ν</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> of electric force to gravitational force between electron and proton,the Avogadro number N</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">,the Gravitational coupling constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> for the electron and the gravitational coupling constant of proton α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G(p)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> ∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=1 (4) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">4.2. Mathematical Formulas that connects 4 dimensionless physical constants </span><span style="background-color: transparent; color: black; font-family: 'Comic Sans MS'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span><span style="background-color: transparent; color: black; font-family: 'Comic Sans MS'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The exact mathematical formula that connects the Proton to Electron Mass Ratio μ,the fine-structure constant α,the ratio Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> of electric force to gravitational force between electron and proton and the Gravitational coupling constant α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> for the electron is:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: left;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;"> α=μ⋅Ν</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;">1</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;">⋅α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;">G </span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;"> (5) </span></p></blockquote></blockquote></blockquote></blockquote></blockquote></blockquote></blockquote><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The exact mathematical formula that connects the Proton to Electron Mass Ratio μ,the fine-structure constant α,the ratio Ν</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> of electric force to gravitational force between electron and proton and the gravitational coupling constant of proton α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G(p)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><p style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;"> α⋅μ=Ν</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;">1</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;">⋅α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;">G(p)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: right; vertical-align: baseline; white-space: pre-wrap;"> (6) </span></p></blockquote></blockquote></blockquote></blockquote></blockquote><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The exact mathematical formula that connects the fine-structure constant α,the ratio Ν</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> of electric force to gravitational force between electron and proton,the Gravitational coupling constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> for the electron and the gravitational coupling constant of proton α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G(p)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> ∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (7) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The exact mathematical formula that connects the Proton to Electron Mass Ratio μ,the fine-structure constant α,the ratio Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> of electric force to gravitational force between electron and proton and the Avogadro number Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (8) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">4.3. Mathematical Formula that connects 5 dimensionless physical constants </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The exact mathematical formula that connects the Proton to Electron Mass Ratio μ,the fine-structure constant α,the ratio Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> of electric force to gravitational force between electron and proton,the Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> and the Gravitational coupling constant α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> for the electron is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅μ⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=1 (9) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The exact mathematical formula that connects the Proton to Electron Mass Ratio μ,the fine-structure constant α,the ratio Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> of electric force to gravitational force between electron and proton,the Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> and the gravitational coupling constant of proton α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν1 (10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The exact mathematical formula that connects the Proton to Electron Mass Ratio μ,the ratio Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> of electric force to gravitational force between electron and proton,the Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">,the Gravitational coupling constant α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> for the electron and the gravitational coupling constant of proton α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ=2⋅e⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1 </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (11) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">4.4. Mathematical formula that connects 6 dimensionless physical constants </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The mathematical Formula that connects the Proton to Electron Mass Ratio μ,the fine-structure constant α,the ratio Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> of electric force to gravitational force between electron and proton,the Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">,the Gravitational coupling constant α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> for the electron and the gravitational coupling constant of proton α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1 </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (12) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">5. New formula </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">5. New formula for Gravitational Constant G </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> The 2.018 CODATA recommended value of Gravitational Constant G is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G=6,67430×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/kg</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">s</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> With standard Uncertainty 0,00015×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/kg</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">s</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> and Relative Standard Uncertainty 2,2x10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">. The Gravitational Constant G is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G=α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙ħ∙c/m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> From (5): </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G=(α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/μ⋅α)⋅(ħ⋅c/m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> From (13): </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G=ħ⋅c/4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So the new formula for Gravitational Constant G is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G=(4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅(ħ⋅c/m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">) (13) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">6. New exact formulas </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">6.1. Correction number </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> We need to find a correction number to have more accurate equations. We propose: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2⋅e≃2⋅e⋅(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (14) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">6.2. New exact formula for the Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> From (2) and (14) the new exact formula for the Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=[(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (15) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">6.3. Mathematical formulas that connects dimensionless physical constants </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> From (4) and (14): </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> ∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=1 (16) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> From (8) and (14): </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (17) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> From (9) and (14): </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅μ⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=1 (18) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> From (10) and (14): </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1 </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (19) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> From (11) and (14): </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ=2⋅e</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1 </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">6.4. Exact mathematical formula that connects 6 dimensionless physical constants </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> From (12) and (14) the exact mathematical formula that connects 6 dimensionless physical constants is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(p)⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1 </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (21) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ=2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">15</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅3</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-26</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅7</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (22) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> So: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α⋅μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-15</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅3</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">26</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅7</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">11</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> (23) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">6.5. New exact Formula for Gravitational Constant G </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> From (13) and (14) the new exact formula for Gravitational Constant G is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: right;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G=[4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅(ħ⋅c/m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">) (24 ) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> With exact value: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G=6,67430×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">/kg</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">s</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">7. Conclusions </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> In this paper are a total of 22 new formulas. Α new formula for the Planck length </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">pℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">ℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">pℓ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">0</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> Α new formula for the Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=(2·e·α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> 9 Mathematical formulas that connect dimensionless physical constants: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α=μ⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">α⋅μ=Ν</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">⋅α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G(p) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> ∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2⋅e⋅α⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅μ⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ=2⋅e⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1 </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1 </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> Α new formula for Gravitational Constant G: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G=(4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅(ħ⋅c/m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> Α new exact formula for the Avogadro number N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=[(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">·α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> 8 exact Mathematical formulas that connect 6 dimensionless physical constants: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> 2</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> ∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅N</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> μ</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">2⋅e</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> ∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅μ⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4⋅e</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">⋅(6⋅7⋅φ/5</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">⋅e)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">⋅α⋅μ⋅α</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">⋅Ν</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">⋅Ν</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ=2⋅e</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">μ=4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">α⋅μ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G(p)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">=2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-15</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅3</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">26</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅7</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">11</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> A new exact formula for Gravitational Constant G: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">G=[4⋅e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅(6⋅7⋅φ/5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅α</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅Ν</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">A</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">⋅(ħ⋅c/m</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13.999999999999998pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">References </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">[1] </span><a href="https://word-edit.officeapps.live.com/we/www.en.wikipedia.org/" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">www.en.wikipedia.org/</span></a><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">[2] </span><a href="https://word-edit.officeapps.live.com/we/www.wolframalpha.com/" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">www.wolframalpha.com/</span></a><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">[3] </span><a href="https://word-edit.officeapps.live.com/we/www.math.stackexchange.com/" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">www.math.stackexchange.com/</span></a><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">[4] </span><a href="https://word-edit.officeapps.live.com/we/www.mathworld.wolfram.com/" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">www.mathworld.wolfram.com/</span></a><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">[5] </span><a href="https://word-edit.officeapps.live.com/we/www.numberempire.com/" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">www.numberempire.com/</span></a><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">[6] </span><a href="http://physics.nist.gov/cuu/Constants/" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">http://physics.nist.gov/cuu/Constants/</span></a><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">[7] Stergios Pellis Unification Archimedes Constant π,Golden Ratio φ,Euler's Number e and Imaginary Number i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><a href="https://vixra.org/pdf/2110.0043v1.pdf" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">https://vixra.org/pdf/2110.0043v1.pdf</span></a><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">, 2.021 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">[8] Stergios Pellis </span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Exact Formula for the Fine Structure Constant α in Terms of the Golden Ratio φ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><a href="https://vixra.org/pdf/2110.0053v1.pdf" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">https://vixra.org/pdf/2110.0053v1.pdf</span></a><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">, 2.021 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">[9] Stergios Pellis Exact Mathematical Expressions of the Proton to Electron Mass Ratio with Symmetrical Shape and Physical Meaning </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><a href="https://vixra.org/pdf/2110.0071v1.pdf" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">https://vixra.org/pdf/2110.0071v1.pdf</span></a><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">, 2.021 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">[10] Jeff Yee The Relationship of the Mole and Charge. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span id="docs-internal-guid-05e0ae92-7fff-2a2e-554c-554a744fa639"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><a href="https://vixra.org/pdf/1904.0445v1.pdf" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">https://vixra.org/pdf/1904.0445v1.pdf</span></a><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">, 2.019</span></p>ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.com0tag:blogger.com,1999:blog-6644102595821010388.post-72367088210186621502021-10-14T15:35:00.001-07:002021-12-26T04:35:44.721-08:00Exact mathematical expressions of the Proton to Electron Mass Ratio with symmetrical shape and physical meaning<p> <span style="background-color: white; font-family: "Comic Sans MS"; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Exact mathematical expressions of the Proton to Electron Mass Ratio with </span><span style="background-color: white; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">symmetrical shape and physical meaning</span></p><span id="docs-internal-guid-14986f75-7fff-e227-0714-ff861ebe0f45"><br /><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="font-family: "Comic Sans MS"; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Stergios Pellis </span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">15/10/2021 </span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Greece </span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Abstract</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> We present 26 </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">exact mathematical expressions of the Proton to Electron Mass Ratio with exact </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">value </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ=1.836,15267343. We propose one exact mathematical expression using Fibonacci and Lucas numbers:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">32</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-42</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·F</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">160</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·L</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">47</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·L</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">19</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">40/19 </span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Also w</span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e present</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">exact mathematical expressions between the Proton to Electron Mass Ratio and mathematical constants and also exact mathematical expressions between the Proton to Electron Mass Ratio and </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">the Fine Structure constant α.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">1. Introduction</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The proton-to-electron mass ratio μ is a ratio of like-dimensioned physical quantities,it is a dimensionless quantity,a function of the dimensionless physical constants,and has numerical value independent of the system of units. Two of the great mysteries of physics are the origin of mass and the mysterious mass ratio between the proton and electron.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The numerical challenge of the mass ratio of proton to electron in the field of elementary particle physics began with the discovery of the electron by JJ Thomson in 1.897,and with the identification of the point nature of the proton by E. Rutherford in 1.911. These two particles have electric charges that are identical in size but opposite charges.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2. Measurement of the Proton to Electron Mass Ratio</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The 2.018 CODATA recommended value of μ is</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ=1.836,15267343 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">With standard Uncertainty</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 0,00000011 </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and Relative Standard Uncertainty</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 6,0×10</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. The value of μ is known at about 0,1 parts per billion. The value of μ is a solution of the equation:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3·μ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-5.508·μ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-841·μ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+10·μ-2.111=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The 2.018 CODATA</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">recommended value of</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> μ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">is</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=m</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">m</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">p</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=0,000544617021487 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">With standard Uncertainty</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 0,000000000000033 </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and Relative Standard Uncertainty</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 6,0×10</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">3. Background of the search for mathematical expression</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-left: -6.75pt; margin-right: -7.275590551181068pt; margin-top: 0pt; margin: 0pt -7.27559pt 0pt -6.75pt; padding: 0pt 0pt 0pt 6.75pt; text-align: justify; text-indent: -6.75pt;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The search for mathematical expression for this dimensionless number motivated many serious scientists. First Peirles in 1.928 proposed the mathematical expression:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ=2·(π-1)·π</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">α </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> A year later Reinhold Furth in 1.929 assumed that μ could be derived from the quadratic equation containing the Fine Structure constant α: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ=64·π</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15·α </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Later in 1.935,A. Eddington,who accepted some of Furth's ideas,presented in his book «New Pathways in Science» the equation for the the Proton to Electron Mass Ratio μ:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10·μ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-136·µ+1=0</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> However both approaches can not be used nowadays as they give very high deviation from the currently known experimental value of µ,so they are not reviewed in present work. Haas in 1.938 presented the expression:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ=3·√2·π</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">α </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Later in 1.951 Lenz noted that μ can be approximated with the formula: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ=6·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> In 1.990,I.J. Good,a British mathematician assembled eight conjectures of numerology for the ratio of the rest masses of the proton and the electron. Recently the professional approach to mathematically decode μ was done by Simon Plouffe. He used a large database of mathematical constants and specialized programs to directly find an expression. Alone with his main remarkable result for the expression for µ via Fibonacci and Lucas numbers and golden ratio he also noted that expression for µ using π can be improved as:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ=6·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+328</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">4. Exact mathematical expression using Fibonacci and Lucas numbers </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Simon Plouffe in his work «A search for a mathematical expression for mass ratios using a large database» proposed the mathematical expression: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=F</span><span style="font-family: Verdana; font-size: 7pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·F</span><span style="font-family: Verdana; font-size: 7pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3/2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·L</span><span style="font-family: Verdana; font-size: 7pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">15/32</span></span><span style="font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/16</span></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> So:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=55·5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3/2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·11</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">15/32</span></span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/16</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">With numerical value μ=1.836,15267481714……</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and Relative Standard Uncertainty</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 1×10</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-9</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. We propose the exact mathematical expression for </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">the Proton to Electron Mass Ratio:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=11</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">47/32</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5/2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·9.349</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5/76</span></span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">21/16</span></span><span style="font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">With exact numerical value μ=1.836,15267343</span><span style="font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">.</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> However: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2·φ-1)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=5 , φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=11 , (φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">19</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-19</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)=9.349</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> So: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">32</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">47</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·(2·φ-1)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">160</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·(φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">19</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-19</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">40/19</span></span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">42 </span></span><span style="font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;"> </span></span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;"> </span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(2)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Also:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">32</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-42</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·F</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">160</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·L</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">47</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·L</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">19</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">40/19 </span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(3)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The formula has an exact value,a symmetrical shape and a greater physical meaning than all types. It seems to be the formula of the Universe.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: white; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">5. Exact mathematical expressions between mathematical constants</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Exact arithmetic mathematical expressions</span><span style="font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">for the Proton to Electron Mass Ratio μ:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) µ=165∙[(ln10)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">11</span></span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">] </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> So:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7∙µ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(5∙13)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙[ln(2∙5)]</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">11 </span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(4)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) µ=1.836+[2∙√77-11)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;"> </span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) µ=2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-12</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-14</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-16</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-17</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-20</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-21</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-23</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-24</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-27</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> (6)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) µ=2∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+4∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+3∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+4∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+8∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+4∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+3∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-12</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> (7) </span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) µ=1.836+(2</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙3∙29</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙7∙521)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;"> </span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(8) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Exact mathematical expressions between the Proton to Electron Mass Ratio μ and </span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Archimedes's constant π</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">:</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) μ=64·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-48·π+8·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+8·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-9</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+6·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-15</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-17</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;"> </span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(9) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) μ=(826·π)-(4.610</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π)-(809</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) </span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;"> </span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) μ=6·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-15</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;"> </span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(11) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Exact mathematical expression between the Proton to Electron Mass Ratio μ and </span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">golden radio φ</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">15</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">12</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-12</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-15</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-17</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-26</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-31</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-34</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;"> </span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(12) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Exact mathematical expression between the Proton to Electron Mass Ratio μ and </span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Euler's number e</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+4·e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-16</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(13) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Exact mathematical expression between the Proton to Electron Mass Ratio μ,</span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Archimedes's constant π </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and </span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">golden radio φ</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">:</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ=[π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-(3.981</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">40)]</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10∙φ </span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(14)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Exact mathematical expression between the Proton to Electron Mass Ratio μ,</span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">golden radio φ </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and </span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Euler's number e</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=477·φ-74·e+446·√2+447·√3-108 </span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(15)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Exact mathematical expression between the Proton to Electron Mass Ratio μ,</span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Archimedes's constant π </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and </span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Euler's number e</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=3·(e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+9·(e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)+495·(e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+11·(e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+11·(e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+22·(e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+11·(e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+8·(e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(16)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Exact mathematical expression between the Proton to Electron Mass Ratio μ,</span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Archimedes's constant π</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">,</span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">golden radio φ </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and </span><span style="font-family: Arial; font-size: 11.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Euler's number e</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=544∙π+493∙φ-463∙e+588 (17)</span></p><br /><p dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: white; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">6. Exact mathematical expressions between </span><span style="font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">the Proton to Electron Mass Ratio,the Fine Structure constant and </span><span style="background-color: white; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">mathematical constants</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Exact mathematical expressions between </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">the Proton to Electron Mass Ratio μ,the Fine Structure constant α and </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">mathematical constants</span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">:</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) μ=398·α+528</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7·π+8 (18)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) μ=(5/7)·(1.224·α+1.287·π-917·φ) (19)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) μ=(1/18)∙(238∙α</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+10∙φ+400) (20)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) µ=6·α</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+360·φ-165·π+345·e+12 (21)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) µ=182·α+141·φ+495·π-66·e+231 (22)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) µ=807·α+1.205·π-518·φ-411·e (23)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) µ=15·α</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-3·Α+9·S-11·K-28·π-23·φ+e-30 (24)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) μ=(1/5)⋅(69⋅α</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+52⋅Q</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Α</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+46⋅π-72⋅φ-46⋅π-111⋅e-27) (25)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) μ=14⋅α</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+10⋅Q</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Α</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+4⋅A-5⋅S-K-17⋅φ-12⋅π-3 (26)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Κ the polygon circumscribing constant with value</span><span style="font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">K</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8,7000366252...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">S</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> the </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">silver constant with value S=2+2</span><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">cos(2</span><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7)=3,246979603717........</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A the Golden Apex</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">with value A</span><span style="font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-7</span><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π-1=0,14954405765........</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Q</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Α</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> the Aristotle’s Quintessence with value Q</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Α</span><span style="font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,0191134319.........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">7. Conclusions</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> All 26 </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">mathematical expressions of the Proton to Electron Mass Ratio have exact </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">value </span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ=1.836,15267343. They have been analysed in terms of their simplicity and numerical significance. We propose these mathematical expressions:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">32</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-42</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·F</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">160</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·L</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">47</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·L</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">19</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">40/19 </span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">32</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">47</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·(2·φ-1)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">160</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·(φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">19</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-19</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">40/19</span></span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">42</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7∙µ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(5∙13)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙[(ln2∙5)</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">11</span></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ=6·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+π</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-15</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">15</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">12</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-12</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-15</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-17</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-26</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-31</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-34</span></span><span style="font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=6·α</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+360·φ-165·π+345·e+12 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=807·α+1.205·π-518·φ-411·e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">µ=15·α</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-3·Α+9·S-11·K-28·π-23·φ+e-30 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">μ=14⋅α</span><span style="font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+10⋅Q</span><span style="font-family: Verdana; font-size: 8pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Α</span><span style="font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+4⋅A-5⋅S-K-17⋅φ-12⋅π-3 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">References </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[1] www.en.wikipedia.org/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[2] www.wolframalpha.com/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[3] www.math.stackexchange.com/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[4] www.mathworld.wolfram.com/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[5] www.numberempire.com/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[6] </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">http://physics.nist.gov/cuu/Constants/</span><span style="background-color: transparent; font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[7] Stergios Pellis Unification Archimedes Constant π,Golden Ratio φ,Euler's Number e and Imaginary Number i</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">https://vixra.org/abs/2110.0043, 2.021 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[8] Stergios Pellis </span><span style="background-color: transparent; font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Exact Formula for the Fine Structure Constant α in Terms of the Golden Ratio φ</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">https://vixra.org/abs/2110.0053, 2.021</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[9] Plouffe S. A search for a mathematical expression for mass ratios using a large database. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">viXra:1409.0099, 2.014</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[10] Alexander Kritov A brief essay on numerology of the mass ratio of proton to electron</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">https://vixra.org/pdf/1410.0105v1.pdf, 2.014</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[11] Michael A. Sherbon Quintessential Nature of the Fine-Structure Constant</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">https://vixra.org/pdf/1709.0083v1.pdf, 2.015</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><div><br /></div></span>ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.com0tag:blogger.com,1999:blog-6644102595821010388.post-57330809496037136032021-10-12T13:07:00.001-07:002021-10-13T13:19:06.428-07:00Unification Archimedes constant π, golden ratio φ, Euler's number e and imaginary number i <p> <span style="font-family: Verdana; font-size: 18pt; font-weight: 700; white-space: pre-wrap;">Unification Archimedes constant π, golden ratio φ, Euler's number e and imaginary number i </span></p><span id="docs-internal-guid-2f829974-7fff-ce3a-e74f-6d5b4fcf8d91"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: center;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Abstract</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">In the first chapter we will present the definitions,history,relations and arithmetics approximations of Archimedes constant π,golden ratio φ,Euler's number e and imaginary number i. A total of 220 expressions.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> In the second chapter we will present exact expressions between Archimedes constant π,golden ratio φ,Euler's number e and imaginary number i. A total of 127 expressions.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> In the third chapter we will present approximations expressions between Archimedes' constant π,the golden ratio φ,the number Euler e and the imaginary number i. A total of 112 expressions.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">1. Basic mathematical constants </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">1.1</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Archimedes constant π</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Introduction </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Archimedes constant π is a mathematical constant that expresses the ratio of the circumference C to the diameter δ of a circle. It is symbolized by the Greek letter π from the middle of the 18th century. It is referred to as Archimedes' constant because the method of determining π is attributed to Greek Mathematician Archimedes from the perimeter P</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">n </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">of a</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">regular polygon with n sides that describe a circle with diameter d. The number π is an implicit and transcendental number. </span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYJl-f8_yLQD0lfnt4bg-Gglqfc0E0G-IU8qfqHfgvoCLmNGRHXT2-g_V3uXQ_DgBxgMPEmD4L9M-a0Pq-9BQYV-VIbXJm6o8vs3gfw1tt_GF49uzZpfOLa6dhB0nf1wHAi5Pq68ebYNw/s512/%25CE%25A3%25CF%2584%25CE%25B1%25CE%25B8%25CE%25B5%25CF%2581%25CE%25AC+%25CF%2580.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="512" data-original-width="384" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYJl-f8_yLQD0lfnt4bg-Gglqfc0E0G-IU8qfqHfgvoCLmNGRHXT2-g_V3uXQ_DgBxgMPEmD4L9M-a0Pq-9BQYV-VIbXJm6o8vs3gfw1tt_GF49uzZpfOLa6dhB0nf1wHAi5Pq68ebYNw/w300-h400/%25CE%25A3%25CF%2584%25CE%25B1%25CE%25B8%25CE%25B5%25CF%2581%25CE%25AC+%25CF%2580.jpg" width="300" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":2,"335551620":2,"335559739":160,"335559740":259}" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #073763; font-family: verdana; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"><b>Archimedes constant π </b></span></td></tr></tbody></table><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> It appears in many types in all fields of mathematics and physics. It is found in many types of trigonometry and geometry,especially in terms of circles, ellipses or spheres. It is also found in various types from other disciplines, such as Cosmology,numbers,Statistics,fractals, thermodynamics,engineering,and electromagnetism. Number is celebrated on the "day of π" and the record of counting the digits of π is often mentioned in news headlines. Several people tried to memorize the value of π as accurately as possible,leading to a record of over 67.000 digits. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">History of Archimedes constant π</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The constant π has been known for almost 4,000 years. The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of π=3. A Babylonian disk in the period 1.900–1.680 BC. indicates a value π=3,125. A papyrus in the period 1.650 BC. gives us a picture of the mathematics of ancient Egypt. The Egyptians calculated the area of a circle with a formula that gave the approximate value π=3,1605. The first calculation of π was made by Archimedes of Syracuse (287-212 BC.X.),one of the greatest mathematicians of the ancient world. Archimedes approached the area of a circle using the Pythagorean Theorem to find the areas of two regular polygons. Archimedes knew that he had not found the value of π but only an approximation within them In this way,Archimedes showed that 3+10/71<π<3+1/7. A similar approach was used by Zu Chongzhi (429–501),a brilliant Chinese mathematician and astronomer. Zu Chongzhi calculated the value of the ratio of the circumference of a circle to its diameter to be 355/113. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Definition </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The constant is defined as: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=C/δ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">C is the circumference C of a circle, </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">δ is the diameter of a circle. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> This definition of π is valid only in flat Euclidean Geometry,while if extended to convex Non-Euclidean Geometries the ratio does not remain constant. There are other definitions of π based on infinite calculus or trigonometry that are not based on a circle. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Numerical value of Archimedes constant π</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> To 50 decimal places the value of Archimedes constant π is:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=3,14159265358979323846264338327950288419716939937510......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> In January 2.020,Timothy Mullican announced the calculation of 50 trillion digits in 303 days. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Exact types of Archimedes constant π </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> An exact formula for the constant π from the inverse tangents of the unit fractions is the Machin formula: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=16·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/5)-4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/239) </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=16·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/5)-4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/239) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Generalized Machin Types: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=20·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/7)+8·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(3/79) </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/√2)+2·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/√8) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">An insignificant monovalent Machin type formula is given by the identity: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Also the type of Euler Machin: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/2)+4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/3) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Also Hermann's formula: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=8·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/2)-4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/7) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Still the Hutton guy: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=8·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/3)+4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1/7) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Three Machin type terms include Gauss's Machin type: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=48·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">18+32·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">57-20·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">239 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Also Strassnitzky's formula: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2-4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5+4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Other types of Machin are: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=24·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8+8·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">57+4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">239 </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=16·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5-4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">70+4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">99 </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=32·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10-4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">239-16·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">515 </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=20·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7+16·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">53+8·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4.443 </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=12·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4+28·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">239+4·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1.985 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Finally other types of Machin by Borwein and Bailey are: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=48·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">49+128·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">57-20·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">239+48·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">110.443 </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=176·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">57+28·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">239-48·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">682+96·tan</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1.296 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Approximations Archimedes constant π </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The 68 arithmetics approximations of Archimedes' constant π are: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) π≃22</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7=3,14...........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) π≃√2+√3≃3,14........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) π≃31</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) π≃19·√2</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">16=3,141........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) π≃(4/5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+7/10=3,141........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) π≃9/5+9</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) π≃(7/3)·(1+√3</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5)=3,141......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) π≃333</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">106=3,1415......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) π≃[(40/3)-√12)])</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) π≃ (3</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">14)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·(193</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) π≃(553</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">312)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12) π≃7</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13) π≃43</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">23</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">14) π≃3+[1</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5·[(2/5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1/2]=3,14159........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15) π≃ln2.198</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">√6=3,14159........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">16) π≃(296</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">167)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,14159........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">17) π≃99</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2.206·√2=3,141592........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">18) π≃4-(106</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">166)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141592........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">19) π≃(689</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">396)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">ln(689</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">396)=3,141592........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">20) π≃(99</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">80)·[7</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/(</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7-3·√2)]=3,141592........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">21) π≃(66</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+86</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">55</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141592........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">22) π≃(47</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+20</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">30</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1=3,141592........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">23) π≃689</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">396·ln(689</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">396)=3,141592......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">24) π≃[(150</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1)/6]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141592........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">25) π≃355</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">113=3,141592........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> With error accuracy</span><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8·10</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. This approximation is the most important because it is expressed in simple fractions and has relatively good accuracy. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">26) π≃(66·√2)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/(</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">33·√29-148)=3,1415926........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">27) π≃2+[1+(413/750)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415926........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">28) π≃(13</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1.181</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1.216</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415926........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">29) π≃(2</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">300</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6·7</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">103</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415926........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">30) π≃(2.143</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">22)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">31) π≃(77.729</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">254)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">32) π≃(9/67)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·ln(5.280)=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">33) π≃103.283</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">32.876=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">34) π≃3·ln(5.280)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">√67=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">35) π≃[9</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+(19</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">22)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> =3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">36) π≃[97+(9</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">22)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">37) π≃ln(π+20-9·10</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-40</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">38) π≃97</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">272</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1.087</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">39) π≃(3</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">√67)·ln(5.280)=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">40) π≃103.993</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">33.102=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">41) π≃22</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">17+37</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">47+88</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">83=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">42) π≃(63/25)+(17+√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/(</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7+√5)=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">43) π≃(63/25)·[(17+15·√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/(</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7+15·√5)=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">44) π≃[31+(62</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+14)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">28</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">45) π≃312.689</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">99.532=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">46) π≃3+(1/7)-1</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[790+(5/6)]=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">47) π≃[31+(25</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3.983)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">48) π≃ln[23+(1/22)+(2/21)]=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">49) π≃427</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">596+405</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">167=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">50) π≃(48/23)·ln(60.318</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13.387)=3,1415926535........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">51) π≃(125/123)·ln(28.102</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1.277)=3,1415926535......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">52) π≃{(19/60)+[1/(3·123.499)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]}</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415926535......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">53) π≃[(19/60)+(3·123.449)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415926535........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">54) π≃2+2</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2/41</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">·(75.757</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1.329)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/41</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,14159265358........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">55) π≃(355</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">113)-[1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(44</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+533)]=3,1415926535897........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">56) π≃(3·√3</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10)·{5-[10</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13-6·(9)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">}</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415926535897........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">57) π ≃{[7+ln(7/12)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1}</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-64=3,1415926535897........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">58) π≃(355</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">113)·[1-(3·10</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3.533)]=3,14159265358979........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">59) π≃(24</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">√142)·ln[(10+11·√2)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+(10+7·√2)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2]=3,14159265358979........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">60) π≃(12</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">√130)·ln[(3+√13)·(√8+√10)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2]=3,14159265358979........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">61) π≃357.377</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(784+105</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">) =3,14159265358979........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">62) π≃(3</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">163</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)·ln(640.320)=3,14159265358979........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">63) π≃[(7+ln7</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-64=3,14159265358979...........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> With error accuracy 2×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-16</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. A relatively simple and very exact expression. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">64) π≃ln(262.537.412.640.768.744)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">√163=3,141592653589793......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">65) π≃(12</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">√190)·ln[(3+√10)·(√8+√10)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2]=3,141592653589793........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">66) π≃2+[(276.694.819.753.963</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">56.647)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/158</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/79</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]=3,1415926535897932........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">67) π≃ln(640.320</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+744)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">163</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,14159265358979323846264338327........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">68) π≃ln[(640.320</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+744)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2·196.884]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(2·163</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=3,1415926535897932384626433832795028841971693993......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Astronomical approximations </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> A strange astronomical approximation is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π≃(1/w)·[(13·y-6·w)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13·y)+3·w] </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">where: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">w =1 week, </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">y=1 year. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> For y=365 days: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=3,1415926 ...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> It is accurate to the first 7 decimal places. For y=365,2425 days,which is the average of the Gregorian year: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π=3,14159 ...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> It is accurate to the first 5 decimal places. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Approximations inequalities </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Also the mathematical constant π can be approached from the inequalities: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3+10/71<π<3+1/7 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> This approach was demonstrated by Archimedes using a polygon with 96 sides. </span></p><p dir="ltr" style="background-color: white; line-height: 1.53781; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">1.2 Golden radio φ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Introduction </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> In mathematics,two quantities have a golden ratio φ if the ratio of their sum to the largest quantity is equal to the ratio of the largest quantity to the smallest. A number that is often encountered when taking distance ratios in simple geometric shapes such as the pentagon,the pentagram,the hexagon and the dodecahedron. The golden ratio φ is a transcendental number. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">History of golden</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">radio φ </span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The ancient Greek mathematicians studied for the first time the golden ratio φ,due to its frequent appearance in geometry. He discovered that the golden ratio was neither an integer nor a fraction. The golden ratio is important in the geometry of regular pentagrams and pentagons. The golden word was known to the Pythagoreans. In their secret symbol,the pentacle,the golden word appears on the sides of a star as well as on the quotient of the area of the regular pentagon with vertices at the edges of the pentagon to the area of the regular pentagon. Pheidias (500 BC-432 BC),the Greek sculptor and mathematician applied the golden ratio φ to the design of sculptures for the Parthenon.</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="background-color: white; margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhn5wGUEMG41NXOKI26bgEJZw1CGKIW-KX_RNjNni0Nzyq_EGL7kW33XaFt5LMuky8MPSqD_K0E1LeGpNqy7M6nMlsXHuTEKwSgzm9RoL6FLXYCVYGRcs0k3DvlfHU-8vPJYW24TECOgVs/s582/%25CE%25A7%25CF%2581%25CF%2585%25CF%2583%25CE%25AE+%25CF%2584%25CE%25BF%25CE%25BC%25CE%25AE.gif" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="507" data-original-width="582" height="349" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhn5wGUEMG41NXOKI26bgEJZw1CGKIW-KX_RNjNni0Nzyq_EGL7kW33XaFt5LMuky8MPSqD_K0E1LeGpNqy7M6nMlsXHuTEKwSgzm9RoL6FLXYCVYGRcs0k3DvlfHU-8vPJYW24TECOgVs/w400-h349/%25CE%25A7%25CF%2581%25CF%2585%25CF%2583%25CE%25AE+%25CF%2584%25CE%25BF%25CE%25BC%25CE%25AE.gif" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="color: #073763; font-family: verdana; font-size: medium;"><b>The chart includes many views of Kepler's golden rectangle and triangle.</b></span></td></tr></tbody></table><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Plato (Circa 428 BC-347 BC),in his views on natural science and cosmology presented in "Timaeus" considered the golden section as the most binding of all mathematical relations and the key to physics Euclid's Elements provide the first written definition of what we now call the golden ratio. Euclid cites one for dividing the line into end and middle ratio. In the 20th century,the golden ratio is represented by the Greek letter φ,from the initial letter of the sculptor Pheidias who is said to have been one of the first to use it in his works. The golden ratio was studied regionally during the next millennium (850–930) used it in the geometric calculations of pentagons and decagones. 18th century mathematicians Abraham de Moivre,Daniel Bernoulli and Leonhard Euler used a formula based on the golden ratio that finds the value of a Fibonacci number with based on its placement in the sequence. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Numerical value of the golden ratio φ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> To 50 decimal places the value of φ is:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=1,61803398874989484820458683436563811772030917980576........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Εxpressions of the golden ratio φ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> In Timaeus,Plato considered the golden ratio φ to be the union of all mathematical relations and the key to the physics of the Universe. The golden ratio φ is a root of the 2nd degree polynomial: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">P (x)=x</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-x-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Both the golden ratio and its conjugates are roots of the 4th degree equation: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">x</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2∙x</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-x</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙x+1=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The basic arithmetic relation applies to the golden ratio φ: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=(√5+1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Other equivalent arithmetic relations for the golden ratio φ are: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=[(√5+3)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=[(5+√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(5-√5)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The following also apply: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=1+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=1+1/φ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=(2+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(2-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ+1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=1+{[1</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[1+(1/φ)]} </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The trigonometric relations also apply to the golden ratio φ: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=-2·sin(666) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=-2·cos(144) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=-2·cos(6∙6∙6) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ=-cos(6∙6∙6)-sin(666) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Also the golden ratio φ satisfies the iteration relation: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2n</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2n-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2n-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">,n ∈ N</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">+</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The following applies to the golden ratio φ: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(1/2)∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+(5/2)∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2=2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+5∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=5∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-4∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+10∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5=(2·φ-1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1)·</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1)=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=5 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6=2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=6 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=7 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-13·φ=5·φ-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=8 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9=2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=9 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10=2∙(2·φ-1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙(φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1)·</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1)=10 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=11 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=12 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">18=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=18 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">29=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=29 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">47=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=47 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">76=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">11</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=76 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">123=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">12</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-12</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">11</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=123 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">199=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">11</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">12</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-12</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=199 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">322=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">12</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-12</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">14</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-14</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=322 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">521=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">15</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-15</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">14</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-14</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=521 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">843=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">14</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-14</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">16</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-16</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">15</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-15</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=843 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1.364=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">15</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-15</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">17</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-17</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">16</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-16</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1.364 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2.207=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">16</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-16</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">18</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-18</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">17</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-17</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2.207 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3.571=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">17</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-17</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">19</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-19</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">18</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-18</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3.571 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5.778=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">18</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-18</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=5.778 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9.349=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">19</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-19</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=9.349 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">271.443=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">26</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-26</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=271.443 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3.010.349=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">31</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-31</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3.010.349 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12.752.043=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">34</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-34</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=12.752.043 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The following also applies to the golden ratio φ: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=89-55·φ=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-12</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=34·φ-55=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-11</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=34-21·φ=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=13·φ-21=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=13-8·φ=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=5·φ-8=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=5·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-13=(2+φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-13=(φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-13=[(φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=5-3·φ=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2·φ-3=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2-φ=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ-1=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2=(2-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">0</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1=0+1=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ=φ+0=1+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ+1=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2·φ+1=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ=2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3·φ+2=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=5·φ+3=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(φ+2)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=8·φ+5=4·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=13·φ+8=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=21·φ+13=7·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+5·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=8·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+5·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=55·φ+34=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">11</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=89·φ+55=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">12</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=144·φ+89=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">11</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">13</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=233·φ+144 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">14</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=377·φ+233 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">15</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=610·φ+377 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">16</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=987·φ+610 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">17</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1.597·φ+987=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">18</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">16</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">18</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2.584·φ+1.597 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">19</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4.181·φ+2.584 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">20</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=6.765·φ+4.181 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Approximations expressions golden ratio φ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 27 approximations expressions golden ratio φ: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) φ≃13</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8=1,6........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) φ≃144</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">89=1,61........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) φ≃89</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">55=1,618........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) φ≃377</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">233=1,6180........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) φ≃521</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">322=1,6180........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) φ≃843</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">521=1,6180........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) φ≃1.597</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">987=1,61803........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) φ≃1.364</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">843=1,61803........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) φ≃4.181</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2.584=1,61803........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) φ≃5.778</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3.571=1,61803........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) φ≃2.207</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1.364=1,618033........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12) φ≃3.571</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2.207=1,618033........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13) φ≃2</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">856</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1.233</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,618033........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">14) φ≃9.349</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5.778=1,6180339........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15) φ≃10.946</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6.765=1,6180339........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">16) φ≃(5.778)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">18</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,6180339........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">17) φ≃(3.571)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">17</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,61803398........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">18) φ≃(9.349)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/19</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,61803398........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">19) φ≃46.368</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">28.657=1,618033988........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">20) φ≃121.393</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">75.025=1,618033988........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">21) φ≃317.811</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">196.418=1,6180339887........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">22) φ≃(1.860.498)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">30</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,618033988749........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">23) φ≃(2.537.720.636)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">45</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,618033988749894........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">24) φ≃(3.461.452.808.002)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">60</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,618033988749894........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">25) φ≃(4.721.424.167.835.364)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">75</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,618033988749894........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">26) φ≃(6.440.026.026.380.244.498)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">90</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,618033988749894........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">27) φ≃7.778.742.049</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4.807.526.976=1,6180339887498948482........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Also the golden ratio φ can be approached from the inequalities: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8/5<φ<81/50 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Golden ratio conjugate Φ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The golden ratio conjugate Φ,also called the silver ratio,is the quantity: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Φ=1/φ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Φ=φ-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Φ=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Φ=(2-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The golden ratio conjugate Φ has value: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Φ =(√5-1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2=2</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(√5+1) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> To 50 decimal places the value of Φ is:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Φ=0,61803398874989484820458683436563811772030917980576 ....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The following applies to the conjunction Φ of the golden ratio φ: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙Φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+5∙Φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.53781; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">1.3 Euler's number e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Introduction </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The number e is an important mathematical constant,which is the base of the natural logarithm. It is the limit of the sequence (1+1/n)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">n</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> as n approaches infinity,an expression derived from the study of compound interest. The number e is sometimes called Euler's number,after the Swiss mathematician Leonhard Euler or Napier's constant.However,Euler's choice of the symbol e is said to have been retained in his honor. The constant was discovered by the Swiss mathematician Jacob Bernoulli while studying compound interest. </span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="background-color: white; margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEyMzowtYQo2Y6g12RPtHi0H2Xt02bHOX-y3GAd_3U6DbVyXoBBlwUg97gT2CxOahTnBhGvQHJDSAwjbIIxoe4iPlarvir94D63zzxK28r0Xk6aOu-9d9BxOzQbBj3o7e-Q9hasMZQ6rM/s357/%25CE%25B1%25CF%2581%25CE%25B9%25CE%25B8%25CE%25BC%25CF%258C%25CF%2582+Euler.gif" style="margin-left: auto; margin-right: auto;"><b><img border="0" data-original-height="218" data-original-width="357" height="244" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEyMzowtYQo2Y6g12RPtHi0H2Xt02bHOX-y3GAd_3U6DbVyXoBBlwUg97gT2CxOahTnBhGvQHJDSAwjbIIxoe4iPlarvir94D63zzxK28r0Xk6aOu-9d9BxOzQbBj3o7e-Q9hasMZQ6rM/w400-h244/%25CE%25B1%25CF%2581%25CE%25B9%25CE%25B8%25CE%25BC%25CF%258C%25CF%2582+Euler.gif" width="400" /></b></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":2,"335551620":2,"335559739":160,"335559740":259}" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-family: verdana; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"><b>The value of <span class="TextRun SCXW99266595 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-family: verdana; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(1+1/n)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-family: verdana; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">n</span></span> n approaches e as n becomes larger.</b></span></td></tr></tbody></table><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Like the constant π,e is irrational (that is,it cannot be represented as a ratio of integers) and transcendental (that is, it is not a root of any non-zero polynomial with rational coefficients). The number e is prominent in mathematics,along with 0,1,π and i. All five of these numbers play important and repetitive roles in mathematics and these five constants appear in a formulation of Euler's identity. Euler's number has many practical uses,especially in higher level mathematics such as calculus,differential equations,trigonometry,complex analysis,statistics,etc. From Euler's identity the following relation of the mathematical constant e can emerge: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e=i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2i/π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">History </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The history of the mathematical constant e begins with John Napier (1.550-1.617) who defined logarithms through a process called dynamic ratio. However,this did not contain the constant itself, but simply a list of logarithms calculated from the constant. that the table was written by William Oughtred. The first known use of the constant,represented by the letter b,was the correspondence from Gottfried Leibniz to Christiaan Huygens in 1,690 and 1,691. However the discovery of the constant itself is credited to Jacob Bernoulli in 1.683</span><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Leonhard Euler introduced the letter e as the basis for natural logarithms, writing in a letter to Christian Goldbach on November 25,1971. Leonhard Euler (1.707-1.783) named his letter after the constant e and discovered many of these remarkable properties. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Numerical value </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> To 50 decimal places the value of e is:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e=2,71828182845904523536028747135266249775724709369995 ............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Approximations expressions</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 26 approximations expressions of Euler's number e</span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) e≃19</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7=2,71................ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) e≃87</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">32=2,718................ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) e≃193</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">71=2,718................ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) e≃1.264</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">465=2,7182............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) e≃878</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">323=2,7182............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) e≃(5</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">93</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,71828............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) e≃3</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+4</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">100</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,71828............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) e≃(355</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">113)-(69/163)=2,71828............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) e≃2.721</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1.001=2,718281............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) e≃(1/7)-[8∙ln(4/5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">ln2]=2,718281............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) e≃3-(5</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">63)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,718281............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12) e≃163</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">32</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">163</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,718281............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13) e≃23.225</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8.544=2,7182818............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">14) e≃2+(54</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+41</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">80</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,7182818............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15) e≃(1+5∙6</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3=2,7182818............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">16) e≃(1+1/80</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)∙(1+1/2+1/3+1/4+1/5+1/6+1/7+1/8)=2,7182818............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">17) e≃(1+9</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">387.420.489</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,71828182............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">18) e≃49.171</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">18.089=2,718281828............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">19) e≃271.801</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">99.990=2,718281828............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">20) e≃517.656</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">190.435=2,7182818284............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">21) e≃[150-(87</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+12</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">83</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,7182818284............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">22) e≃(37/613)∙[45+(35/991)]=2,7182818284............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">23) e≃[8</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(9.112.774</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-52)]=2,71828182845............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">24) e≃4-[(300</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-100</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1.291</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+9</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">91</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]=2,718281828459............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">25) e≃[1.097-(55</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+311</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-11</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">68</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,718281828459045............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">26) e≃848.456.353</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">312.129.649=2,71828182845904523............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Also the constant e can be approached from the inequalities: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2+7/10<e<2+3/4 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">1.4 Imaginary unit i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Introduction </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The imaginary unit i is a solution to the quadratic equation x</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1=0. Although there is no real number with this property,i can be used to extend the real numbers to what are called complex numbers,using addition and multiplication. Despite their misleading name,imaginary numbers are not only real but also very useful,with application in electricity,signal processing and many other applications. They are widely used in electronics,for the representation of alternating currents and in waves.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">History</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Although the Greek mathematician and engineer Hero of Alexandria is noted as the first to have conceived imaginary numbers,it was Rafael Bombelli who first set down the rules for multiplication of complex numbers in 1.572. The concept had appeared in print earlier,such as in work by Gerolamo Cardano. At the time,imaginary numbers and negative numbers were poorly understood and were regarded by some as fictitious or useless much as zero once was. Many other mathematicians were slow to adopt the use of imaginary numbers,including René Descartes,who wrote about them in his La Géométrie in which the term imaginary was used and meant to be derogatory. The use of imaginary numbers was not widely accepted until the work of Leonhard Euler (1.707–1.783) and Carl Friedrich Gauss (1.777–1.855). The geometric significance of complex numbers as points in a plane was first described by Caspar Wessel (1.745–1.818).</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Εxpressions of imaginary unit i</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The imaginary unit i has the ability:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=−1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The square root of i is:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">√i=±(i+1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> For the imaginary unit i: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4n</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4n+1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4n+2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4n+3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=-i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">η is any integer.Also:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">cosi=(e+1/e)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2∙e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">sini=(e-1/e)∙i</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2=(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1)∙i</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2∙e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">1.5 Other numbers</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Gelfond's constant </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Gelfond's constant,in mathematics,is the number e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">,e raised to the power π. Like e and π,this constant is a transcendental number. It was named after the Soviet mathematician Aleksandr Gelfond. Gelfond's constant were singled out in Hilbert's 7th problem as an example of numbers whose excess was an open problem. This was first established by Gelfond and may now be considered as an application of the Gelfond–Schneider theorem,noting that:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(-1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The numerical value Gelfond's constant is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃23,14069263277926900572.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 17 approximations expressions Gelfond's constant: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃2∙(4∙π-1)=23,1..... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃23+π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1-e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=23,1....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃20+π=23,14..... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃162</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7=23,14..... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙[3+(4+√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">])</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=23,140......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃302∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">41=23,140...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃3.241∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">440=23,1406...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃[29</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">42+(9.507)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]=23,14069...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃30+(1+√2)-345</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7=23,140692...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃ln3+(159/5)∙ln2=23,14069263...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃7∙π+1+(-e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+28∙e+189</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">634∙e)=23,1406926327...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃6.112.351∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">829.816=23,140692632779...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃7∙π+(365.455</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">317.913)=23,140692632779...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">14) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃17+√3+(172))</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+ln(ln9)=23,1406926327792...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃20+π+1</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[1.111+1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(11+1/√2)]=23,1406926327792...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">16) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃(421∙π-133∙φ-316)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(-176∙π+539∙φ-285)=23,14069263277926......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">17) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃(-381∙π+363∙φ+469∙e+127)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(44∙π+11∙φ+88∙e-361)=23,140692632779260057......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Number i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The number i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">is:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-π/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="color: #202122; font-family: Arial; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The decimal expansion is given by:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃0,20787957635076190854...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Number π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The decimal expansion for π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is given by:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃22,45915777183610454734......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> It is not known whether or not this number is transcendental.For Gelfond's constant e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and number π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃2=2,000893…...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Number e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">-π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The decimal expansion for e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> is given by: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃0,68153491441822353230........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Other numbers</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃2,178457567938.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃4,53475716116............ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃3,69902532658.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃6,37951853648.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃5,04316564336........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃9,8787760564777.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃85,59800812326............ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃101,84682653935........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃104,93742163059........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.53781; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2. Exact</span><span style="background-color: transparent; font-family: Verdana; font-size: 20pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">expressions between mathematical constants</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.1 Exact expressions between φ and π </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 47 exact expressions between golden ratio φ and Archimedes constant π:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) φ=2∙cos(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) φ=2∙sin(3∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) φ=1</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2∙cos(2π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) φ=1</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2∙sin(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) φ=-2∙cos(4∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) φ=1-2∙cos(3∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) φ=(1/2)∙sec(2∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) φ=(1/2)∙csc(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) φ=sin(3∙π/10)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">sin(π/6) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) φ=sin(π/6)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">sin(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) φ=sin(2∙π/5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">sin(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12) φ=sin(5π/6)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">sin(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13) φ=sin(7∙π/10)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">sin(π/6) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">14) (3-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15) (φ∙√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">16) cos(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1+φ)+cos(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ)=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">17) φ=[π+(5∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2∙π </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">18) (2-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(2∙π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">19) [2-(1/φ)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(3∙π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">20) [2+(1/φ)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">21) (2+φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">22) (2-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">23) (2-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">24) (2+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(3∙π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">25) (2+φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(2∙π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">26) [2+(2+φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">27) [2+(2+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">28) [2+(2-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(3∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">29) [2+(2-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">30) [2-(2-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(3∙π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">31) [2-(2-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(7∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">32) [2-(2+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(2∙π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">33) [2-(2+φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(9∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">34) [2+(2+φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(9∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">35) [2+(2+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(2∙π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">36) [2+(2-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(7∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">37) [2+(2-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(3∙π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">38) [2-(2-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">39) [2-(2-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(3∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">40) [2-(2+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">41) [2-(2+φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙sin(π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">43) φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+(3∙φ∙√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4∙cos(π/15) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">44) (φ∙√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙cos(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">45) φ+(3∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4∙cos(2∙π/15) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">46) -φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+(3∙φ∙√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4∙cos(4∙π/15) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">47) -φ+(3∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4∙cos(7∙π/15) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.2 Exact expressions between φ and e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 11 exact relationships between golden ratio φ and Euler's number e: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) e=(2</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ-1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2/ln(5)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) φ=(1+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) φ=</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">(1/2)ln(φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ-1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) φ=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln(-1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-ln(-1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">(1/2)ln(φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ-1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln(-1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-ln(-1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">(1/2)ln(φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ-1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln(-1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-ln(-1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) φ=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">(1/2)ln(φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ-1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 21pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1+φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 21pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1+φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 21pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 21pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.3 Exact expressions between π and e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 8 Exact relationships between Archimedes constant π and Euler's number e: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) </span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4∙cos(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) </span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4∙sin(3∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) </span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1-4∙cos(3∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) </span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=sec(2∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) </span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=csc(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) 2∙sin(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5)=[3-</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">½</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) cos[π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1+</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2)]+cos[2∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)]=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">={[π+(5∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π}-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.4 Exact expressions between π and i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 3 exact relationships between Archimedes constant π and imaginary unit i: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) π=2∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) π=2∙i∙log(1-i</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1+i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) π=-i∙ln(-1) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.5 Exact expressions between φ and i</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 14 exact relationships between golden ratio φ and imaginary unit i: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+i∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(1+2∙i)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+i∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2∙[1+(i/2)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) 2∙sin(i∙lnφ)=i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) sin</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(i∙lnφ)=-1/4 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) φ=[ln(cosφ+i∙sinφ)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) 2∙sin(i∙lnφ)=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-lnφ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">lnφ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) 2∙sin(i∙lnφ)=-i∙[(1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ)-φ] </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) φ=2∙cos(2∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) φ=2∙sin(3∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) φ=1-2∙cos(6∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) φ=(1/2)∙sec(4∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12) φ=(1/2)∙csc(lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13) 2∙sin(2∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i)=(3-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">14) cos(2∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1+φ)+cos(2∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i∙φ)=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.6 Exact expressions between e and i</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 11 exact expressions between Euler's number e and imaginary unit i: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) cosi=(e+1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2∙e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) sini=(e-1)∙i</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2∙e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1=2∙i∙e∙sini </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) sini=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-e</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2∙i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-e=2∙i∙sini </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) </span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4∙cos(2∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) </span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4∙sin(3∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) </span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1-4∙cos(6∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) </span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=sec(4∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) </span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=csc(lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) 2∙sin(2∙lni</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙i)=[3-</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ln5/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.7 Exact expressions between π,φ and i </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 4 exact expressions between golden ratio φ,Archimedes constant π and imaginary unit i:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) sin[(π/2)-i∙lnφ]=√5</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) i∙π=ln(φ)+ln(1-φ) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) π=-5∙i∙log{(1/2)∙[φ+i∙(4-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]} </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) φ=</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(2</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ-1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5ln(5)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(2</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ-1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5ln(5)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.8 Exact expressions between φ,e and i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 3 exact expressions between golden ratio φ,Euler's number e and imaginary unit i:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iφ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=cosφ+i∙sinφ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) φ=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2lni</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2lni</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iφ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=cos(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2lni</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2lni</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)+i∙sin(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2lni</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2lni</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.9 Exact expressions between φ,π and e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 3 exact relationships between golden ratio φ,Archimedes constant π and Euler's number e: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) 2∙cos(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">(1/2)ln(φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ-1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) 2∙cos(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5)=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) φ=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">{ln[2cos(π/5)]+ln(2φ-1)}</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-iπ{ln[2cos(π/5)]+ln(φ-1)}</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.10 Exact expressions between π,e and i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 10 exact expressions between Archimedes constant π,Euler's number e and imaginary unit i: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) e=i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2i/π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-π/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> =</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=cosπ+i·sinπ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(-1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=√5 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.11 Exact expressions between π,φ,e and i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 16 exact expressions that connects golden ratio φ,Archimedes constant π,Euler's number e and imaginary unit i:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iφ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i(φ+2π)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iφ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iφ+2iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iφ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=cos(φ+2∙π)+i∙sin(φ+2∙π) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) φ=e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) φ=i∙[(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ/10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(1-e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)] </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ/10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-iπ/10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=i/φ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) 2∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ+i∙(3-φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) 2∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=φ+i∙(√5/φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) φ=2∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2∙i∙sin(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ/10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(i</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2∙φ)+(1-1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12) φ=(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13) φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">14) φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15) φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=-(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-24iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">16) φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-iπ/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)+1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> These relationships are the most important in mathematics because they connect the four basic mathematical constants.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">2.12 Exact Magic expression that connects six basic mathematical constants 0,1,π,φ,e and i</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> The following expression connects six basic mathematical constants,the number 0,the number 1,golden ratio φ,Archimedes constant π,Euler's number e and imaginary unit i:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1+φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1+φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-iπ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.53781; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">3. Αpproximations expressions between mathematical constants</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">3.1 Αpproximations expressions between φ and π </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 25 approximations expressions that connects the golden ratio φ and Archimedes constant π:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) π≃φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">(π+φ)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,14.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) φ≃2∙(log</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π)-π=1,61......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) π≃4</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">√φ=3,14.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) π≃6∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1)=3,141......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) φ≃(π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2π-6)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,618........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) π≃3∙(φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5=3,141......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) π≃6∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5=3,141.........</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;"> </span></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) φ≃(5∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,6180........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) (12/7)∙logπ-2∙logφ≃1=0,99997044.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) [2∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]-[(√2-1)∙4</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π]≃0=0,000470957.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) π≃(6/5)∙log2+(24/5)∙logφ=3,14159......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12) π≃(48∙φ-37)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8∙φ=3,141592......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13) φ≃37</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(48-8∙π)=1,6180339.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">14) π≃[(802∙φ-801)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(602∙φ-601)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415926......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15) π≃(2</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙5</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙4.463</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9.181∙φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415926......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">16) φ≃2</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙5</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙4.463</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9.181∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,6180339.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">17) π≃(9.764.064φ+4.867.832</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">944.055φ+566.433)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141592653............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">18) φ≃4.867.832-566.433∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">944.055∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-9.764.064=1,618033988........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">19) φ≃ln(3∙π∙22</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">35)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">ln[(111∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/8)+(2/21)]=1,61803398874........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">20) φ≃(355</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">113∙π)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4/565</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙9349</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2/35</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,61803398874........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">21) π≃(35</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3∙22</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)·[360·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+(3∙φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141592653............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">22) π≃(14.212.169</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)-φ=3,1415926535897.............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">23) φ≃(14.212.169</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)-π=1,6180339887498........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">24) φ≃151.837.964∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">294.810.267=1,6180339887498948482........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">` </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">25) φ≃11∙(40∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+23∙π-70)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(502∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-659∙π-185)=1,6180339887498948482........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">3.2 Αpproximations expressions between π and e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 45 approximations expressions that connects Archimedes constant π and Euler's number e:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) π≃2∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">√3=3,1.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) π≃128</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15∙e=3,1.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.53781; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) π≃7∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">cos(5/2)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,14..........</span></p><p dir="ltr" style="background-color: white; line-height: 1.53781; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"> </p><p dir="ltr" style="background-color: white; line-height: 1.53781; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) π≃(163)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(e)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-6=3,14......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) </span><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Π</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃(4∙e-1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,14..........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) e≃9-2∙π=2,71......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.53781; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) π≃e+tan(2/5)=3,141......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) π≃3</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">sin(3∙e)=3,141........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) π≃(2∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141.........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) π≃[e</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(π-e)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141.........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) e≃(π+1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,718........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃10=9,999838798..........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-π≃20=19,999099979..........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">14) 3</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">(π+e)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃5=4,999973083............ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-</span><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-Π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃0=0,000017673.........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">16) (π+e+163)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃13=12,994609439........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">17) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1-e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃23=23,00081238.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">18) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2∙(4∙π-1)≃0=0,007951404......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">19) (163/e)+(e/163)+(π/163)-60=0,000299061......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">20) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙[3+(4+√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">])</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=23,140406827........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">21) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃2=2,000893…....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">22) π≃2∙7</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(5-e/5)=3,1415......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">23) π≃ln[(7-e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2]=3,14159......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">24) e≃(5</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">93</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,71828............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">25) π≃[(2+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,14159.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">26) π≃(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/3)+(19/28)=3,14159.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">27) π≃(69</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">163)+e=3,14159.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">28) π≃(920</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">157)-e=3,14159........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">29) π≃ln[e∙ln(4.979)]=3,141592........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">30) π≃[lnln(97+7/5)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141592......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">31) π≃e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">75.709</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 21pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">66.137</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415926.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">32) π≃2+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">709</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5.354</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,1415926........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">33) e≃42∙π∙[(π/2)-ln(3∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2)]=2,71828182.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">34) e≃2.100∙(10</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">629)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,71828182.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">35) π≃10∙tanh(28∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15)</span><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-(Π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)≃0=0,0000000006005.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">36) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-ln3-(159/5)∙ln2≃0=0,00000000023.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">37) e≃(1,000924472)∙[2∙(4/π)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">(π/4)4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,718281828............ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">38) (3.730∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e)-(879∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 13pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-419</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">.736≃0=0,0000000001622........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">39) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-π/9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4π/9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-9π/9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-16π/9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-25π/9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-36π/9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-49π/9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-64π/9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1≃0=0,0000000000010504..... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">40) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-7∙π-1-(-e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+28∙e+189</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">634∙e)≃0,000000000000377311....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">41) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-7∙π-(365.455</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">317.913)≃0=0,00000000000002805671....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">42) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-{20+π+1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[1.111+1/(11+1/√2)]}≃0=0,000000000000063.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">43) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-[17+√3+(172))</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+ln(ln9)]≃0=0,000000000000025........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">44) e≃[π-(12</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">ln889)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1/4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> With numerical value for Euler's number e=2,7182818284590........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">45) π≃(12</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">ln889)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> With numerical value for Archimedes constant π=3,14159265358979...........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> We observe that these relatively simple relationships with error 2×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-19 </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">have amazing accuracy.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">3.3 Αpproximations expressions between φ and e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 11 approximations expressions that connects golden ratio φ and Euler's number e:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) φ≃(5∙e+4)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4∙e=1,61.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) e≃4</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(4∙φ-5)=2,71........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) e≃φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-13</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,7182......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) e≃φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">(φ+1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙2</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">(φ+1)</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,7182......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) φ≃(2</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6/e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-4)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,6180............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) e≃6⋅7⋅φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,7182........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) φ≃5</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6⋅7=1,6180............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) 1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e+1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ+1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">71≃1=0,999997937........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) 1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">√e+1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">87≃1=0,999990924............ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) φ≃[√63∙(3-e)+1]</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2=1,61803......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) φ≃(711∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-906∙e-487)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(175∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-56∙e+283)=1,6180339887498948482....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">3.4 Αpproximation expression between π and i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 1 approximations expressions that connects Archimedes constant π and imaginary unit i:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) (π+20)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">3.5 Αpproximations expressions between φ,π and e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 28 approximations expressions that connects golden ratio φ,Archimedes constant π and Euler's number e:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) e≃(φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-</span><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π/e</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,71........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2) φ≃357∙π-412∙e=1,61......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3) e≃3∙φ-π+1=2,71......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4) (φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-(3/2)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">12</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃0=0,000286948.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5) φ≃e-(π)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/12</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,618.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6) e≃π+φ+(1-π∙φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2=2,718........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7) π≃[(6∙e∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">8) π≃[φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-(1</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3,141....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">9) π≃5∙φ∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">7=3,141....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10) e≃π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">12/7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,7182........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) e≃[(2∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙π-φ-1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3]-π∙φ=2,7182.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">12) e≃7∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=2,7182........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">13) φ≃[7∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">6∙e]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,6180........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">14) φ≃7∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙e=1,6180....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">15) e≃7∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5∙φ=2,7182........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">16) e≃(6∙φ-2∙π+2∙π∙φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5=2,71828........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">17) φ≃[5∙(1+π)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e]-6=1,6180339........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">18) π≃[</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙(φ+6)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">5]-1=3,1415926......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">19) φ≃14∙(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">19</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">22</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,6180339......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">20) π≃(2∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(e-1)-[(2∙φ-1)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(100-36/10</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)]=3,1415926535.........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">21) φ≃14∙(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">19</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">22</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙(10∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/531</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=1,6180339887.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">22) (φ+e)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">314.393.388.446.503</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">402.909.889.100.000</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃1,0000000000000018.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">23) (φ+e))</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">314.393.388.446.503</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">402.909.889.100.000</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃π=3,14159265358979......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">24) φ≃(1.967.981∙π-314.270∙e)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">3.293.083=1,618033988749894...........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">25) e≃1.400∙φ-2.410∙π+1.082</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">906∙φ-1.016∙π+172=2,71828182845904523.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">26) φ≃-π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2∙π-3∙e-13+√2-log2-log3</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-3∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-π-e+7∙√2+7∙√3-3∙log2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> With numerical value for golden ratio φ=1,618033988749894848........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">27) φ≃(1/42)∙[22∙π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-56∙e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+50∙π-34∙e-5∙(1+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+7∙(1+e)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+20∙(1+π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-24∙(1+π)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1] </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> With numerical value for golden ratio φ=1,6180339887498948482........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">28) e≃(45.483∙φ-2.961∙π-18.765)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">16.748 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> This approximation has the highest accuracy with a numerical value for the Euler's number e=2,718281828459045235360.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">3.6 Αpproximation expression between i,π and e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 1 approximation expression that connects Archimedes constant π,Euler's number e and imaginary unit i:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1) π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">ie</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1≃2=1,99977658867............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">3.7 Αpproximation expression between φ,i,π and e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> 1 approximation expression that connects golden ratio φ,Archimedes constant π,Euler's number e and imaginary unit i:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+(i</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e)]</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Conclusions</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">We presented new exact and approximations expressions that connects golden ratio φ,Archimedes constant π,Euler's number e and imaginary unit i.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">References </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[1] </span><a href="https://www.blogger.com/blog/post/edit/6644102595821010388/1474806249132171021#" style="text-decoration-line: none;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">www.en.wikipedia.org/</span></a><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[2] </span><a href="https://www.blogger.com/blog/post/edit/6644102595821010388/1474806249132171021#" style="text-decoration-line: none;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">www.wolframalpha.com/</span></a><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[3] www.</span><a href="https://www.blogger.com/blog/post/edit/6644102595821010388/1474806249132171021#" style="text-decoration-line: none;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">math.stackexchange.com/</span></a><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[4] www.mathworld.wolfram.com/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[5] www.numberempire.com/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[6] http://www.contestcen.com/pi.htm </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[7] https://archive.lib.msu.edu/crcmath/math/math/p/p303.htm </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[8] https://archive.lib.msu.edu/crcmath/math/math/e/e001.htm </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[9] https://www.primepuzzles.net/puzzles/puzz_050.htm </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[10] Panagiotis Stefanides http://www.stefanides.gr/Html/pi.html </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[11] Frank Michael Jackson Extending Euler's identity to include Phi, the golden ratio</span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">www.researchgate.net/publication/292983417_Extending_Euler's_identity_to_include_Phi_the_golden_ratio </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[12] Binh Ho On the Approximate Relationship between Pi, Euler's Number, and the Golden Ratio Constant </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">DOI: </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10.13140/RG.2.2.17490.91843 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[13] William H. Press Seemingly Remarkable Mathematical Coincidences Are Easy to Generate </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">https://web.archive.org/web/20120312092311/http://www.nr.com/whp/NumericalCoincidences.pdf </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[14] Michele Nardelli,Antonio Nardelli On the Ramanujan's Fundamental Formula for obtain a highly precise Golden Ratio: mathematical connections with Black Holes Entropies and Like-Particle Solutions </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">https://vixra.org/pdf/1909.0456v1.pdf </span></p><div><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div></span>ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.com0tag:blogger.com,1999:blog-6644102595821010388.post-37247840479064767362021-10-12T12:14:00.000-07:002021-10-13T13:36:18.617-07:00 Exact formula for the Fine Structure constant α in terms of the Golden Ratio φ <p> <span style="font-family: "Comic Sans MS"; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; text-align: justify; vertical-align: baseline; white-space: pre-wrap;">Exact formula for the Fine Structure constant α in terms of the Golden Ratio φ</span><span style="font-family: "Comic Sans MS"; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: justify; vertical-align: baseline; white-space: pre-wrap;"> </span></p><span id="docs-internal-guid-0dac9235-7fff-441c-6809-56b4d02b8378"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Stergios Pellis</span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">13/10/2021 </span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: center;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Greece </span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Abstract</span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.5893181818181819; margin-bottom: 0pt; margin-right: 9.561023622047287pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> We propose the exact formula for the Fine Structure constant α in terms of the Golden Ratio φ: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">α</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=360·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+(3</span><span style="background-color: transparent; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 8.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Introduction</span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Dr. Rajalakshmi Heyrovska has found that the Golden Ratio φ provides a quantitative link between various known quantities in atomic physics,research in this book chapter entitled "The Golden ratio in the creations of Nature arises in the architecture of atoms and ions". While searching for the exact values of ionic radii and for the significance of the ionization potential of hydrogen,Dr. Heyrovska has found that the Bohr radius can be divided into two Golden sections pertaining to the electron and proton. More generally,it was found that φ is also the ratio of anionic to cationic radii of any atom,their sum being the covalent bond length. After that she showed,among other facts,that many bond lengths in organic and inorganic molecules behave additively,and are the sum of the covalent and the ionic radii,whether partially or fully ionic or covalent. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> A new interpretation and a very accurate value of the fine structure constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> has been discovered in terms of the Golden Angle. Dr. Heyrovska proposed another interpretation of α based on the observation that it is close to the Golden Angle. Fine Structure constant can also be formulated for the first time exclusively in terms of the Golden Ratio as follows: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">α</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=360·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=137,03562809...... (1) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Measurement of Fine Structure constant</span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The 2.018 CODATA recommended value of α is: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">α</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=q</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">4</span><span style="background-color: transparent; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">π</span><span style="background-color: transparent; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">ε</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">0</span><span style="background-color: transparent; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">ħ</span><span style="background-color: transparent; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">c</span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=0.0072973525693(11) (2) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> With standard Uncertainty 0,0000000011×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;"> </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and Relative Standard Uncertainty 1,5×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">For reasons of convenience,historically the value of the reciprocal of the fine-structure constant is often specified. The 2.018 CODATA recommended value is given by: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">α</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">= 137,035999084(21). (3) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> With standard Uncertainty</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">0,000000021×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;"> </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and Relative Standard Uncertainty 1,5×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">There is general agreement for the value of α,as measured by these different methods. The preferred methods in 2.019 are measurements of electron anomalous magnetic moments and of photon recoil in atom interferometry. The most precise value of α obtained experimentally (as of 2.012) is based on a measurement of g using a one-electron so-called "quantum cyclotron" apparatus,together with a calculation via the theory of QED that involved 12.672 tenth-order Feynman diagrams: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">α</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=137,035999174(35). (4) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> This measurement of α has a relative standard uncertainty of</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2,5</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">×</span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">10</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-10</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 10pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">.</span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> This value and uncertainty are about the same as the latest experimental results. Further refinement of this work were published by the end of 2.020,giving the value: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> α</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=137,035999206(11). (5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">with a relative accuracy of 81 parts per trillion. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Exact formula for the Fine Structure constant α</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> There is a dream,which,albeit more often not confessed,occupies the most secret aspirations of theoreticians and is that of reducing the various constants of Physics to simple formula involving integers and transcendent numbers. We propose the exact formula for the Fine Structure constant α in terms of the Golden Ratio φ: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">α</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">=360·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">-2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">+(3</span><span style="background-color: transparent; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5 </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(6) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">with numerical value: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">α</span><span style="background-color: transparent; font-family: Verdana; font-size: 15pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=137,03599916476564.......... (7) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> This numerical value is the average of the measurements (3),(4) and (5).</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> We believe that the formula (6) is </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">the exact formula for the Fine Structure constant α.</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Conclusions</span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">We presented new Exact formula for the Fine Structure constant α in terms of the Golden Ratio φ: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">α</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=360·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+(3</span><span style="background-color: transparent; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 9.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">References </span><span style="background-color: transparent; font-family: "Comic Sans MS"; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[1] www.en.wikipedia.org/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[2] www.wolframalpha.com/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[3] www.math.stackexchange.com/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[4] www.mathworld.wolfram.com/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[5] www.numberempire.com/ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[6] </span><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">http://physics.nist.gov/cuu/Constants/</span><span style="background-color: transparent; font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[7] Heyrovska,R. Golden Ratio Based Fine Structure Constant and Rydberg Constant for Hydrogen Spectra. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[8] Heyrovska,R. The Golden ratio,ionic and atomic radii and bond lengths. Molecular Physics,103,877-882 (2.005) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[9] Heyrovska,R. The Golden ratio in the Creations of Nature Arises in the Architecture of Atoms and Ions. Chapter 12 in Book:"Innovations in Chemical Biology",Editor:Bilge Sener,Springer.com,January (2009). </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[10] Heyrovska,R. and Narayan,S. Atomic Structures of Molecules Based on Additivity of Atomic and/or Ionic Radii. AIP Conference Proceedings 1119,216 (2.009)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">http://precedings.nature.com/documents/3292/version/1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[11] Heyrovska,R.Dependence of the Length of the Hydrogen Bond on the Covalent and Cationic Radii of Hydrogen,and Additivity of Bonding Distances. Chemical Physics Letters,432,348-351 (2.006). </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">[12] Heyrovska,R. Fine-structure Constant,Anomalous Magnetic Moment,Relativity Factor and the Golden Ratio that Divides the Bohr Radius. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">http://arxiv.org/ftp/physics/papers/0509/0509207.pdf </span></p><div><span style="background-color: transparent; font-family: Verdana; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div></span>ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.com0tag:blogger.com,1999:blog-6644102595821010388.post-14748062491321710212021-10-07T13:59:00.016-07:002021-10-10T09:48:26.772-07:00Ενοποίηση της σταθεράς του Αρχιμήδη π,της χρυσής τομής φ,του αριθμού Euler e και του φανταστικού αριθμού i <p><span id="docs-internal-guid-277d8367-7fff-4b77-2b99-e4241eda9e96"></span></p><p dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-right: 16.6476pt; margin-top: 0pt;"><span style="background-color: transparent; font-family: Verdana; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: red; font-size: x-large;">Ενοποίηση της σταθεράς του Αρχιμήδη π,της χρυσής τομής φ,του αριθμού Euler e και του φανταστικού αριθμού i </span></span></p><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{dc9f949e-b7c0-4dc8-9fa8-51fa84082c5f}{159}" paraid="1908800387" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: center; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":2,"335551620":2,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{dc9f949e-b7c0-4dc8-9fa8-51fa84082c5f}{163}" paraid="939098111" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: center; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; font-weight: bold; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":2,"335551620":2,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{dc9f949e-b7c0-4dc8-9fa8-51fa84082c5f}{167}" paraid="411402978" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; font-weight: bold; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1.Βασικές μαθηματικές σταθερές</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{dc9f949e-b7c0-4dc8-9fa8-51fa84082c5f}{173}" paraid="2023312962" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; font-weight: bold; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{dc9f949e-b7c0-4dc8-9fa8-51fa84082c5f}{177}" paraid="555807362" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1.1 Σταθερά </span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">του Αρχιμήδη</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> π</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{dc9f949e-b7c0-4dc8-9fa8-51fa84082c5f}{187}" paraid="171608497" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{dc9f949e-b7c0-4dc8-9fa8-51fa84082c5f}{191}" paraid="793876329" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Εισαγωγή</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{dc9f949e-b7c0-4dc8-9fa8-51fa84082c5f}{197}" paraid="228278961" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{dc9f949e-b7c0-4dc8-9fa8-51fa84082c5f}{201}" paraid="1542176467" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: left; vertical-align: baseline; white-space: pre-wrap;">Η σταθερά του Αρχιμήδη π είναι μια μαθηματική σταθερά που εκφράζει τον λόγο της περιφέρειας C προς τη διάμετρο του δ ενός κύκλου. Συμβολίζεται με το ελληνικό γράμμα π από τα μέσα του 18ου αιώνα. Αναφέρεται ως σταθερά του Αρχιμήδη γιατί η μέθοδος προσδιορισμού του π αποδίδεται στον Έλληνα Μαθηματικό Αρχιμήδη από την περίμετρο P</span><span style="background-color: transparent; font-family: Verdana; font-size: 9pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: left; vertical-align: baseline; white-space: pre-wrap;">n</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: left; vertical-align: baseline; white-space: pre-wrap;"> ενός κανονικού πολυγώνου με n πλευρές που περιγράφουν έναν κύκλο με διάμετρο δ. Ο αριθμός π είναι ένας άρρητος και υπερβατικός αριθμός. </span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYJl-f8_yLQD0lfnt4bg-Gglqfc0E0G-IU8qfqHfgvoCLmNGRHXT2-g_V3uXQ_DgBxgMPEmD4L9M-a0Pq-9BQYV-VIbXJm6o8vs3gfw1tt_GF49uzZpfOLa6dhB0nf1wHAi5Pq68ebYNw/s512/%25CE%25A3%25CF%2584%25CE%25B1%25CE%25B8%25CE%25B5%25CF%2581%25CE%25AC+%25CF%2580.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="512" data-original-width="384" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYJl-f8_yLQD0lfnt4bg-Gglqfc0E0G-IU8qfqHfgvoCLmNGRHXT2-g_V3uXQ_DgBxgMPEmD4L9M-a0Pq-9BQYV-VIbXJm6o8vs3gfw1tt_GF49uzZpfOLa6dhB0nf1wHAi5Pq68ebYNw/w300-h400/%25CE%25A3%25CF%2584%25CE%25B1%25CE%25B8%25CE%25B5%25CF%2581%25CE%25AC+%25CF%2580.jpg" width="300" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-family: verdana; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Σταθερά του Αρχιμήδη π.</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":2,"335551620":2,"335559739":160,"335559740":259}" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-family: verdana; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></td></tr></tbody></table><p></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{dc9f949e-b7c0-4dc8-9fa8-51fa84082c5f}{236}" paraid="568086091" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> </span></span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Εμφανίζεται σε πολλούς τύπους σε όλους τους τομείς των Μαθηματικών και της Φυσικής,όπως και σε πολλούς τύπους της Τριγωνομετρίας και της Γεωμετρίας,ειδικά όσον αφορά κύκλους,ελλείψεις ή σφαίρες. Βρίσκεται επίσης και σε διάφορους τύπους από άλλους κλάδους της επιστήμης,όπως η Κοσμολογία,η Θεωρία των αριθμών,η Στατιστική,τα Fractals,η Θερμοδυναμική,η Μηχανική,και ο Ηλεκτρομαγνητισμός. Ο καθολικός χαρακτήρας του π τον καθιστά μια από τις πιο ευρέως γνωστές μαθηματικές σταθερές,τόσο εντός όσο και εκτός της επιστημονικής κοινότητας και έχει αποτελέσει θέμα λογοτεχνικών βιβλίων. Ο αριθμός π γιορτάζεται την «ημέρα του π» και ρεκόρ υπολογισμού των ψηφίων του π συχνά αναφέρονται σε τίτλους ειδήσεων. Αρκετοί άνθρωποι προσπάθησαν να απομνημονεύσουν την τιμή του π με όσο το δυνατόν μεγαλύτερη ακρίβεια,οδηγώντας σε ρεκόρ απομνημόνευσης πάνω από 67.000 ψηφία.</span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{47}" paraid="1153262390" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{51}" paraid="2004607759" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-77333f91-7fff-fa0f-8375-e9dcaad646c9"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">Ιστορία της σταθεράς του Αρχιμήδη π </span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{61}" paraid="1147874565" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{65}" paraid="542507460" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Η σταθερά π είναι γνωστή για σχεδόν 4.000 χρόνια. Οι αρχαίοι Βαβυλώνιοι υπολόγισαν την έκταση ενός κύκλου λαμβάνοντας 3 φορές το τετράγωνο της ακτίνας του,το οποίο έδωσε μια τιμή π=3. Ένας βαβυλωνιακός δίσκος την περίοδο 1.900–1.680 π.Χ. υποδεικνύει μια τιμή π=3,125. Μια πάπυρος την περίοδο 1.650 π.Χ. μας δίνει μια εικόνα για τα μαθηματικά της αρχαίας Αιγύπτου. Οι Αιγύπτιοι υπολόγισαν την περιοχή ενός κύκλου με έναν τύπο που έδωσε την κατά προσέγγιση τιμή π=3,1605. Ο πρώτος υπολογισμός του π έγινε από τον Αρχιμήδη των Συρακουσών (287-212 π.Χ.),έναν από τους μεγαλύτερους μαθηματικούς του αρχαίου κόσμου. Ο Αρχιμήδης προσέγγισε την περιοχή ενός κύκλου χρησιμοποιώντας το Πυθαγόρειο Θεώρημα για να βρει τις περιοχές δύο κανονικών πολυγώνων. Ο Αρχιμήδης ήξερε ότι δεν είχε βρει την τιμή του π αλλά μόνο μια προσέγγιση εντός αυτών των ορίων. Με αυτόν τον τρόπο,ο Αρχιμήδης έδειξε ότι 3+10/71<π<3+1/7. Μια παρόμοια προσέγγιση χρησιμοποιήθηκε από τον Zu Chongzhi (429–501),έναν λαμπρό Κινέζο μαθηματικό και αστρονόμο. Ο Zu Chongzhi υπολόγισε την τιμή της αναλογίας της περιφέρειας ενός κύκλου προς τη διάμετρο του να είναι 355/113. Οι μαθηματικοί άρχισαν να χρησιμοποιούν το ελληνικό γράμμα π το 1.700. Παρουσιάστηκε από τον William Jones το 1.706,η χρήση του συμβόλου διαδόθηκε από τον Leonhard Euler,ο οποίος το υιοθέτησε το 1.737. Ο Γάλλος μαθηματικός Georges Buffon του δέκατου όγδοου αιώνα επινόησε έναν τρόπο υπολογισμού του π βάσει της πιθανότητας. </span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{159}" paraid="203686833" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{163}" paraid="909028768" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Ορισμός</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{169}" paraid="1607587034" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{173}" paraid="1674866865" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Η σταθερά π ορίζεται ως:</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{179}" paraid="1998395041" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{183}" paraid="1068451779" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">π=C/δ</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{191}" paraid="983698089" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{195}" paraid="2008122315" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">C η περιφέρεια C ενός κύκλου,</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{201}" paraid="1494775756" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">δ η διάμετρο ενός κύκλου.</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{207}" paraid="406621367" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> </span></span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;">Αυτός ο ορισμός του π είναι έγκυρος μόνο σε επίπεδη Ευκλείδεια Γεωμετρία,ενώ αν επεκταθεί σε κυρτές Μη-Ευκλείδειες Γεωμετρίες ο λόγος δεν παραμένει σταθερός. Υπάρχουν άλλοι ορισμοί του π με βάση τον απειροστικό λογισμό ή την Τριγωνομετρία που δεν βασίζονται σε κύκλο. </span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{213}" paraid="417718304" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{217}" paraid="511153718" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Αριθμητική τιμή</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{223}" paraid="840546395" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{227}" paraid="586611402" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Η αριθμητική τιμή του π στα πρώτα ενενήντα δεκαδικά ψηφία του είναι:</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{233}" paraid="2069443512" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{237}" paraid="458567260" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">π=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534...</span></span></p><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{237}" paraid="458567260" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;"><br /></span></p><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{237}" paraid="458567260" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;"> Τον Ιανουάριο του 2.020,ο Timothy Mullican ανακοίνωσε τον υπολογισμό των 50 τρισεκατομμυρίων ψηφίων σε διάστημα 303 ημερών. </span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span id="docs-internal-guid-8a68e4dd-7fff-ed96-3055-bba49a69feb2"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">Ακριβείς τύποι της σταθεράς του Αρχιμήδη π </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Ένας ακριβής τύπος για την σταθερά π από τις αντίστροφες εφαπτομένες των κλασμάτων μονάδας είναι ο τύπος του Machin: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=16·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/5)-4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/239) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=16·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/5)-4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/239) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Γενικευμένοι τύποι Machin: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=20·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/7)+8·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(3/79) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/√2)+2·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/√8) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Μια ασήμαντη μονοδύναμη φόρμουλα τύπου Machin δίνεται από την ταυτότητα: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Επίσης ο τύπος του Euler Machin: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/2)+4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/3) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Επίσης ο τύπος του Hermann: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=8·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/2)-4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/7) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Ακόμα ο τύπος του Hutton: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=8·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/3)+4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1/7) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Τρεις όροι τύπου Machin τύπου περιλαμβάνουν τον τύπο Gauss's Machin: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=48·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">18+32·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">57-20·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">239 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Επίσης ο τύπος του Strassnitzky: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2-4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5+4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Άλλοι τύποι Machin είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=24·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8+8·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">57+4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">239 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=16·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5-4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">70+4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">99 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=32·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10-4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">239-16·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">515 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=20·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7+16·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">53+8·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4.443 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=12·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4+28·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">239+4·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1.985 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Τέλος άλλοι τύποι Machin από τους Borwein και Bailey είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=48·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">49+128·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">57-20·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">239+48·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">110.443 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=176·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">57+28·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">239-48·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">682+96·tan</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1.296 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">Προσέγγισεις της σταθεράς π </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p class="Paragraph SCXW60264244 BCX0" paraeid="{78540cd4-30e8-44cf-bce3-96378166f14d}{249}" paraid="750387803" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-2d3b186f-7fff-2a55-b86a-1ef9b7e2c2af"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Οι 68 αριθμητικές προσέγγισεις της σταθεράς π είναι:</span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{2}" paraid="1546998186" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{6}" paraid="1804122120" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1) π≃22</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">7=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,14...........</span></span></p><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{6}" paraid="1804122120" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><br /></span></span></p><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{6}" paraid="1804122120" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Αυτή η προσέγγιση ήταν γνωστή στον Αρχιμήδη.</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{20}" paraid="1784089395" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{24}" paraid="1376726278" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2) π≃√2+√3≃</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,14</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{34}" paraid="297782893" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{38}" paraid="746249135" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3) π≃31</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,141</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{56}" paraid="846401159" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{60}" paraid="321221193" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">4) π≃19·√2</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">16</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,141</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{76}" paraid="189240441" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{80}" paraid="1503540578" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5) π≃(4/5)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-4</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+7/10=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,141</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{94}" paraid="1673868064" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{98}" paraid="1827133061" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">6</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π≃9/5+9</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,141</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{118}" paraid="976296485" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{122}" paraid="938429227" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">7</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π≃(7/3)·(1+√3</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,141</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">.........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{140}" paraid="110878564" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{144}" paraid="1305312643" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">8</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃333</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">106=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,1415</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">.........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{162}" paraid="1196444649" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{166}" paraid="1917316359" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">9</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π≃[(40/3)-√12</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)]</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,1415</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">.........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{186}" paraid="863870696" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{190}" paraid="1846468404" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">10</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π≃ (3</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">14)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·(193</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,1415</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{218}" paraid="1831566535" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{222}" paraid="530641051" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">11) π≃(553</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">312)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,1415</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{240}" paraid="2014753427" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{f771b852-da3c-44ae-a1eb-6c1399350587}{244}" paraid="119690257" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">12) π≃7</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">7</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">4</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">9</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,1415</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{9}" paraid="1413328887" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{13}" paraid="1574189516" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">13</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃43</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">7</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">23</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3,1415...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{31}" paraid="126195167" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{35}" paraid="2036319519" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">14) π≃3+[1</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5·[(2/5)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/10</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+1/2]=3,14159...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{49}" paraid="2016565551" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{53}" paraid="1683111440" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">15</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π≃ln2.198</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">√6=3,14159...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{65}" paraid="1274738277" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{69}" paraid="1152190209" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">16</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π≃(296</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">167)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,14159</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{89}" paraid="1514589609" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{93}" paraid="301521490" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">17</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃99</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2.206·√2=3,141592...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{109}" paraid="727223532" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{113}" paraid="1184797086" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">18</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃4-(106</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">166)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/3</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3,141592...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{131}" paraid="178947582" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{135}" paraid="89693040" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">19</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π≃(689</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">396)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="SpellingError SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-image: url("data:image/gif;base64,R0lGODlhBQAEAJECAP////8AAAAAAAAAACH5BAEAAAIALAAAAAAFAAQAAAIIlGAXCCHrTCgAOw=="); background-position: 0% 100%; background-repeat: repeat-x; border-bottom: 1px solid transparent; margin: 0px; padding: 0px; user-select: text;">ln</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(689</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">396)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3,141592...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{159}" paraid="1927516968" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{163}" paraid="1606927448" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">20</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃(99</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">80)·[7</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/(</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">7-3·√2)]=3,141592...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{181}" paraid="1828555698" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{185}" paraid="399325201" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">21</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π≃(66</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+86</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">55</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3,141592...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{209}" paraid="415074714" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{213}" paraid="682859030" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">22</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π≃(47</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+20</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">30</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-1=3,141592...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{237}" paraid="459338599" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{7f7c2561-64aa-4c46-bcae-d86e8c8afb58}{241}" paraid="992482060" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">23</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) </span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">π≃</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">689</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">396</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">ln(689</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">396)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,141592.........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{14}" paraid="1109649521" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{18}" paraid="991210712" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">24</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) </span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">π≃[(150</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3/2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-1)/6]</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/5</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3,141592...........</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{40}" paraid="496814599" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{44}" paraid="1632516755" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">25</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃355</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">113=3,141592...........</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> </span></span></span></p><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{44}" paraid="1632516755" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"><br /></span></span></span></p><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{44}" paraid="1632516755" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">Μ</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">ε</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> ακρίβεια σφάλμα</span></span><span class="TextRun SCXW60264244 BCX0" color="windowtext" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">τος</span><span class="TextRun SCXW60264244 BCX0" color="windowtext" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 10.5pt; font-variant-ligatures: none; line-height: 18.3458px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span><span class="TextRun SCXW60264244 BCX0" color="windowtext" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">8·10</span><span class="TextRun SCXW60264244 BCX0" color="windowtext" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-8</span></span><span class="TextRun SCXW60264244 BCX0" color="windowtext" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">. Αυτ</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">ή η προσέγγιση είναι η πιο σημαντική γιατί εκφράζεται με απλό κλάσμα και έχει σχετικά καλή ακρίβεια.</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{78}" paraid="1035273172" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{82}" paraid="1282672993" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">26) π</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃(66·√2)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/(</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">33·√29-148)=3,1415926...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{94}" paraid="1614523188" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{98}" paraid="416376984" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">27) π</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃2+[1+(413/750)]</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3,1415926...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{110}" paraid="1648992243" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{114}" paraid="1780526097" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">28) π</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃(13</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">4)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1.181</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1.216</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3,1415926...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{134}" paraid="2080605940" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{138}" paraid="1802889414" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">29) π≃(2</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">300</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6·7</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">103</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/5</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3,1415926...........</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{162}" paraid="2107945885" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{166}" paraid="216276812" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">30</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) </span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">π</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃(2.143</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">22)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/4</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,14159265</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{190}" paraid="173491812" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{194}" paraid="915914726" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">31</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) </span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">π</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃(77.729</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">254)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/6</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,14159265</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{218}" paraid="1577432138" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{222}" paraid="1624283175" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">32</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π≃(9/67)</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·ln(5.280)=3,14159265...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{234}" paraid="1717278154" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{59dc5d72-14a4-44c2-a577-069bef727273}{238}" paraid="1389940216" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">33</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃103.283</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">32.876=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,14159265</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{3a0a016a-1a8b-4d91-813b-e3b7dc94cc5f}{1}" paraid="1652959910" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{3a0a016a-1a8b-4d91-813b-e3b7dc94cc5f}{5}" paraid="1907914004" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">34</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃3·ln(5.280)</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">√67=3,14159265...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{3a0a016a-1a8b-4d91-813b-e3b7dc94cc5f}{19}" paraid="1461185834" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{3a0a016a-1a8b-4d91-813b-e3b7dc94cc5f}{23}" paraid="603026004" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">35</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃[9</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+(19</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">22)]</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/4</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> =</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,14159265</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{3a0a016a-1a8b-4d91-813b-e3b7dc94cc5f}{51}" paraid="1592286706" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{3a0a016a-1a8b-4d91-813b-e3b7dc94cc5f}{55}" paraid="394133444" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">36</span><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) π</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃[97+(9</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">22)]</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW60264244 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/4</span></span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3,14159265</span><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...........</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{3a0a016a-1a8b-4d91-813b-e3b7dc94cc5f}{77}" paraid="490948533" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">37) π≃ln(π+20-9·10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-40</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">38) π≃97</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">272</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1.087</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">39) π≃(3</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">√67)·ln(5.280)=3,14159265........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">40) π≃103.993</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">33.102=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">41) π≃22</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">17+37</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">47+88</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">83=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">42) π≃(63/25)+(17+√5)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/(</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7+√5)=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">43) π≃(63/25)·[(17+15·√5)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/(</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7+15·√5)=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">44) π≃[31+(62</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+14)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">28</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">45) π≃312.689</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">99.532=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">46) π≃3+(1/7)-1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">[790+(5/6)]=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">47) π≃[31+(25</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3.983)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">48) π≃ln[23+(1/22)+(2/21)]=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">49) π≃427</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">596+405</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">167=3,141592653........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">50) π≃(48/23)·ln(60.318</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">13.387)=3,1415926535........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">51) π≃(125/123)·ln(28.102</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1.277)=3,1415926535......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">52) π≃{(19/60)+[1/(3·123.499)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]}</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,1415926535......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">53) π≃[(19/60)+(3·123.449)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,1415926535........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">54) π≃2+2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2/41</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">·(75.757</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1.329)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/41</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,14159265358........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">55) π≃(355</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">113)-[1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(44</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+533)]=3,1415926535897........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">56) π≃(3·√3</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10)·{5-[10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">13-6·(9)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">}</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,1415926535897........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">57) π ≃{[7+ln(7/12)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+1}</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-64=3,1415926535897........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">58) π≃(355</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">113)·[1-(3·10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3.533)]=3,14159265358979........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">59) π≃(24</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">√142)·ln[(10+11·√2)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+(10+7·√2)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2]=3,14159265358979...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">60) π≃(12</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">√130)·ln[(3+√13)·(√8+√10)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2]=3,14159265358979........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">61) π≃357.377</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(784+105</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">) =3,14159265358979........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">62) π≃(3</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">163</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)·ln(640.320)=3,14159265358979........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">63) π≃[(7+ln7</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">12)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+1]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-64=3,14159265358979...........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Mε ακρίβεια σφάλματος 2×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-16</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">. Μια σχετικά απλή και πολύ ακριβής έκφραση. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">64) π≃ln(262.537.412.640.768.744)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">√163=3,141592653589793......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">65) π≃(12</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">√190)·ln[(3+√10)·(√8+√10)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2]=3,141592653589793........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">66) π≃2+[(276.694.819.753.963</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">56.647)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/158</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/79</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]=3,1415926535897932....</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">67) π≃ln(640.320</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+744)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">163</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,14159265358979323846264338327..... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">68) π≃ln[(640.320</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+744)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-2·196.884]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(2·163</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Με αριθμητική τιμή:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p class="Paragraph SCXW60264244 BCX0" paraeid="{3a0a016a-1a8b-4d91-813b-e3b7dc94cc5f}{81}" paraid="982211216" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-c832da39-7fff-cd66-0c9d-9db31771714e"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=3,1415926535897932384626433832795028841971693993......... </span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{9038d6e1-c47f-4a15-a604-f03a1de292cc}{148}" paraid="956483085" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">Αστρονομική προσέγγιση </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Mια περίεργη αστρονομική προσέγγιση είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π≃(1/w)·[(13·y-6·w)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">13·y)+3·w] </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">όπου: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">w=1 εβδομάδα, </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">y=1 χρόνος. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Για y=365 ημέρες: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=3,1415926...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;"> Είναι ακριβής στα πρώτα 7 δεκαδικά ψηφία. Για y=365,2425 ημέρες,που είναι ο μέσος όρος του Γρηγοριανού έτους: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π=3,14159...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p class="Paragraph SCXW60264244 BCX0" paraeid="{9038d6e1-c47f-4a15-a604-f03a1de292cc}{152}" paraid="2049019658" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-f8066f73-7fff-9b7b-3758-8e944f2f3977"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Είναι ακριβής στα πρώτα 5 δεκαδικά ψηφία. </span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{17}" paraid="579148877" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{21}" paraid="1296793291" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Προσεγγιστικές ανισότητες</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{27}" paraid="1615195837" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{31}" paraid="245163894" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Επίσης η μαθηματική σταθερά π μπορεί να προσεγγιστεί από τις ανισότητες:</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{37}" paraid="499997144" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{41}" paraid="219729191" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3+10/71<π<3+1/7</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{45}" paraid="1058484080" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW60264244 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW60264244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: white; clear: both; cursor: text; direction: ltr; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW60264244 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{49}" paraid="555327882" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; font-size: 12px; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW60264244 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Αυτή την προσέγγιση την απέδειξε ο Αρχιμήδης χρησιμοποιώντας ένα πολύγωνο με 96 πλευρές.</span><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p><p class="Paragraph SCXW60264244 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{49}" paraid="555327882" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; font-size: 12px; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-family: verdana; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"><br /></span></p><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{59}" paraid="685804158" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1.2 Χρυσή τομή φ</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{65}" paraid="224759078" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{69}" paraid="602115320" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Εισαγωγή</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{75}" paraid="754540704" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #202122; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #202122; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{79}" paraid="1821118477" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #202122; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;">Στα μαθηματικά,δύο ποσότητες έχουν αναλογία χρυσής τομής φ αν ο λόγος του αθροίσματος τους προς τη μεγαλύτερη ποσότητα είναι ίσος με το λόγο της μεγαλύτερης ποσότητας προς τη μικρότερη.</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhn5wGUEMG41NXOKI26bgEJZw1CGKIW-KX_RNjNni0Nzyq_EGL7kW33XaFt5LMuky8MPSqD_K0E1LeGpNqy7M6nMlsXHuTEKwSgzm9RoL6FLXYCVYGRcs0k3DvlfHU-8vPJYW24TECOgVs/s582/%25CE%25A7%25CF%2581%25CF%2585%25CF%2583%25CE%25AE+%25CF%2584%25CE%25BF%25CE%25BC%25CE%25AE.gif" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="507" data-original-width="582" height="349" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhn5wGUEMG41NXOKI26bgEJZw1CGKIW-KX_RNjNni0Nzyq_EGL7kW33XaFt5LMuky8MPSqD_K0E1LeGpNqy7M6nMlsXHuTEKwSgzm9RoL6FLXYCVYGRcs0k3DvlfHU-8vPJYW24TECOgVs/w400-h349/%25CE%25A7%25CF%2581%25CF%2585%25CF%2583%25CE%25AE+%25CF%2584%25CE%25BF%25CE%25BC%25CE%25AE.gif" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><span style="color: #073763; font-family: verdana; font-size: medium;">Το διάγραμμα περιλαμβάνει πολλές εμφανίσεις του χρυσού ορθογωνίου και του τριγώνου του Kepler.</span></b></td></tr></tbody></table><p></p><p class="Paragraph SCXW210773143 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{79}" paraid="1821118477" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;"> Η χρυσή τομή ή χρυσός λόγος,επίσης γνωστός ως θεϊκή αναλογία,χρυσός μέσος όρος είναι ένας αριθμός που συναντάται συχνά κατά τη λήψη των αναλογιών αποστάσεων σε απλά γεωμετρικά σχήματα όπως το πεντάγωνο,το πεντάγραμμα,το δεκαγώνο και το δωδεκάεδρο. Ο αριθμός φ είναι ένας υπερβατικός αριθμός. </span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{106}" paraid="1305566686" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: center; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":2,"335551620":2,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{110}" paraid="82267288" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Ιστορία της χρυσής τομής</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{116}" paraid="1742076436" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{120}" paraid="1364324780" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> </span></span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Οι αρχαίοι Έλληνες μαθηματικοί μελέτησαν για πρώτη φορά την χρυσή τομή φ,λόγω της συχνής εμφάνισής της στη γεωμετρία. Ο μαθηματικός Ίππασος τον 5ο αιώνα π.Χ. ανακάλυψε ότι η χρυσή αναλογία δεν ήταν ούτε ακέραιος αριθμός ούτε κλάσμα. Η χρυσή αναλογία είναι σημαντική στη γεωμετρία των κανονικών πενταγράμμων και πενταγώνων. Η αντίληψη αυτή αποδίδεται συνήθως στον Πυθαγόρα και τους ακολούθους του και λέγεται ότι η σχετική θεωρία διατυπώθηκε για πρώτη φορά από την πυθαγόρεια φιλόσοφο Θεανώ. Ο χρυσός λόγος ήταν γνωστός στους Πυθαγόρειους. Στο μυστικό τους σύμβολο,την πεντάλφα,ο χρυσός λόγος εμφανίζεται στις πλευρές τους αστεριού καθώς και στο πηλίκο του εμβαδού του κανονικού πενταγώνου με κορυφές τις άκρες της πεντάλφα προς το εμβαδόν του κανονικού πενταγώνου που σχηματίζεται εντός του αστεριού. Ο Φειδίας (500 π.Χ.-432 π.Χ.),ο Έλληνας γλύπτης και μαθηματικός εφάρμοσε την χρυσή τομή φ στο σχεδιασμό γλυπτών για τον Παρθενώνα. Ο Πλάτωνας (περίπου το 428 π.Χ.-347 π.Χ.),στις απόψεις του για τη φυσική επιστήμη και την κοσμολογία που παρουσιάστηκε στο «Τίμαιο» θεώρησε το χρυσό τμήμα ως το πιο δεσμευτικό όλων των μαθηματικών σχέσεων και το κλειδί για τη φυσική του κόσμου. Τα Στοιχεία του Ευκλείδη παρέχουν τον πρώτο γραπτό ορισμό αυτού που σήμερα ονομάζουμε χρυσή τομή. Ο Ευκλείδης παραθέτει μια για το χώρισμα της γραμμής σε άκρο και μέσο λόγο. Σε όλα τα Στοιχεία αρκετές προτάσεις και οι αποδείξεις τους εμπεριέχουν τον χρυσό λόγο. Από τον 20ό αιώνα,η χρυσή τομή παριστάνεται με τον ελληνικό γράμμα φ,από το αρχικό γράμμα του γλύπτη Φειδία ο οποίος λέγεται ότι ήταν από τους πρώτους που τον χρησιμοποίησε στα έργα του. Η χρυσή αναλογία μελετήθηκε περιφερειακά κατά την επόμενη χιλιετία. Ο Abu Kamil (850–930) το χρησιμοποίησε στους γεωμετρικούς υπολογισμούς των πενταγώνων και δεκαγώνων. Τα γραπτά του επηρέασαν αυτό του Fibonacci (1.170–1.250),ο οποίος χρησιμοποίησε την αναλογία σε συναφή προβλήματα γεωμετρίας,αν και δεν το συνέδεσε ποτέ με τη σειρά αριθμών που πήρε το όνομά του. Οι μαθηματικοί του 18ου αιώνα Abraham de Moivre,Daniel Bernoulli και Leonhard Euler χρησιμοποίησαν έναν τύπο με βάση τη χρυσή αναλογία που βρίσκει την αξία ενός αριθμού Fibonacci με βάση την τοποθέτησή του στην ακολουθία. </span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{1}" paraid="950579165" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{5}" paraid="1452515643" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Σχέσεις της </span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">χρυσής τομής φ</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{13}" paraid="740709504" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{17}" paraid="826635685" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> </span></span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;"> Στον Τίμαιο,ο Πλάτωνας θεωρούσε την χρυσή τομή φ ένωση όλων των μαθηματικών σχέσεων και το κλειδί για τη φυσική του Κόσμου.Η χρυσή τομή φ είναι μια ρίζα του 2ου βαθμού πολυωνύμου: </span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{27}" paraid="1713519888" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{31}" paraid="1190011910" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">P(x)=x</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">−x−1</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{41}" paraid="1636657876" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{45}" paraid="1890521449" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Τόσο η χρυσή τομή όσο και οι συζυγείς του είναι ρίζες της 4ου βαθμού εξίσωσης: </span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{51}" paraid="405622724" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{55}" paraid="1595584770" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">x</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">−2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">x</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">−x</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">x+1=0</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{81}" paraid="1871659241" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{85}" paraid="731511986" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Για την χρυσή τομή φ ισχύει η βασική αριθμητική σχέση:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{91}" paraid="821911951" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{95}" paraid="108538122" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=(√5+1)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{105}" paraid="909096531" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{109}" paraid="1279897735" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Άλλες ισοδύναμες αριθμητικές σχέσεις για την χρυσή τομή φ είναι:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{115}" paraid="747634712" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{119}" paraid="1355786922" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=[(√5+3)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2]</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{131}" paraid="21876078" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{135}" paraid="585649375" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=[(5+√5)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(5-√5)]</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{147}" paraid="1042051277" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{151}" paraid="120301800" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Επίσης ισχύουν οι σχέσεις:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{157}" paraid="51315969" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{161}" paraid="238197635" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=1+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{169}" paraid="1833517009" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{173}" paraid="777081377" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=1+1/φ</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{179}" paraid="557517380" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{183}" paraid="1116833330" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=(2+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{197}" paraid="767668738" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{201}" paraid="1684409098" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=(2-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{217}" paraid="1486600090" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{221}" paraid="30913375" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ+1</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{231}" paraid="1531716303" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{235}" paraid="1616327936" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=1+{[1</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">[1+(1/φ)]}</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{245}" paraid="60783439" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{249}" paraid="1280275051" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Επίσης για την χρυσή τομή φ ισχύουν οι τριγωνομετρικές σχέσεις:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{4c5c19c0-a89b-4ce5-b9f1-ecb1b62be494}{255}" paraid="428648556" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{4}" paraid="1858041504" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=-2·sin(666)</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{10}" paraid="1345245814" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{14}" paraid="10478843" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=-2·cos(144)</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{20}" paraid="666300684" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{24}" paraid="853506230" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=-2·cos(6</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6)</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{38}" paraid="212885766" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{42}" paraid="1133330610" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-49cdfffd-7fff-37d7-2bdc-21e8ed6bcd45"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">φ=-cos(6∙6∙6)-sin(666) </span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{60}" paraid="359496114" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{64}" paraid="977439227" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Επίσης η χρυσή τομή φ ικανοποιεί την σχέση επανάληψης:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{70}" paraid="2012373096" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{74}" paraid="1147639834" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2n</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2n-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2n-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">,n</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #050505; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> ∈</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> N</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">+</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{98}" paraid="1078664081" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{102}" paraid="578670556" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Για τη χρυσή τομή φ ισχύουν οι σχέσεις:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{108}" paraid="770749980" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{112}" paraid="1802414216" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=(1/2)∙φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+(5/2)∙φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{170}" paraid="1847685045" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{174}" paraid="925350959" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2=2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+5</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{224}" paraid="1109601482" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{13ec3d93-b4b0-4533-9d89-27786ae074a9}{228}" paraid="1040490182" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{230e1d32-9072-49de-9e93-69fb8945c22d}{19}" paraid="400391100" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{230e1d32-9072-49de-9e93-69fb8945c22d}{23}" paraid="2100142486" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">4=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-</span><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=4</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-4</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+10</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=4</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{230e1d32-9072-49de-9e93-69fb8945c22d}{119}" paraid="892481680" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{230e1d32-9072-49de-9e93-69fb8945c22d}{123}" paraid="323568636" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5=(2·φ-1)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=(φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+1)·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+1)=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=5</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{230e1d32-9072-49de-9e93-69fb8945c22d}{161}" paraid="1789943452" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{230e1d32-9072-49de-9e93-69fb8945c22d}{165}" paraid="1385958425" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6=2·φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+2·φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=6</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{230e1d32-9072-49de-9e93-69fb8945c22d}{195}" paraid="977326169" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{230e1d32-9072-49de-9e93-69fb8945c22d}{199}" paraid="2015845835" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">7=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=7</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{230e1d32-9072-49de-9e93-69fb8945c22d}{229}" paraid="1409491772" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{230e1d32-9072-49de-9e93-69fb8945c22d}{233}" paraid="511397164" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">8=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-13</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=5</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=8</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{20}" paraid="1642911709" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{24}" paraid="1194032621" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">9=2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=9</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{88}" paraid="1631322653" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{92}" paraid="97373322" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">10=2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(2·φ-1)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+1)·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+1)=10</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{122}" paraid="1914530510" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{126}" paraid="2070567206" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">11=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">6</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-6</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=11</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{156}" paraid="584541958" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{160}" paraid="701539952" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">12=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=12</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{182}" paraid="803727066" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{186}" paraid="1813439291" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">18=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">6</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-6</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">8</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-8</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">18</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{220}" paraid="651243443" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{a78c2ce5-d174-43e0-948e-b75c70629db0}{224}" paraid="1715692885" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">29=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">9</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-9</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">8</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-8</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">29</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{3}" paraid="1274576447" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{7}" paraid="1312927751" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">47=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">8</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-8</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">10</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-10</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">9</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-9</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">47</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{41}" paraid="2080904336" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{45}" paraid="1825676933" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">76=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">9</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-9</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">11</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-11</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">10</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-10</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">76</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{79}" paraid="66437409" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{83}" paraid="1237218705" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">123=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">10</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-10</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">12</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-12</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">11</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-11</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">123</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{117}" paraid="332636677" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{121}" paraid="432492604" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">199=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">11</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-11</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">13</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-13</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">12</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-12</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">199</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{155}" paraid="1238126808" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{159}" paraid="121491719" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">322=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">12</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-12</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">14</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-14</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">13</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-13</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">322</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{193}" paraid="1871887845" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{197}" paraid="466048283" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">521=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">13</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-13</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">15</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-15</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">14</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-14</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">521</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{231}" paraid="2038495859" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{9dac7cc5-d32a-4ad1-9fba-a682b032da84}{235}" paraid="128898728" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">843=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">14</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-14</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">16</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-16</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">15</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-15</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=843</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{10}" paraid="1094239102" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{14}" paraid="1170191977" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1.364=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">15</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-15</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">17</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-17</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">16</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-16</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">1.364</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{48}" paraid="1586831185" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{52}" paraid="531347005" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2.207=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">16</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-16</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">18</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-18</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">17</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-17</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">2.207</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{86}" paraid="1188547244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{90}" paraid="815610472" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3.571=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">17</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-17</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">19</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-19</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">18</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-18</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3.571</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{120}" paraid="1578531742" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{124}" paraid="920878753" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5.778=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">18</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-18</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=5.778</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{138}" paraid="1037148695" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{142}" paraid="1525354120" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">9.349=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">19</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-19</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=9.349</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{156}" paraid="1895991842" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{160}" paraid="2017945607" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">271.443=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">26</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-26</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=271.443</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{174}" paraid="2004502025" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{178}" paraid="2028668180" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3.010.349=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">31</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-31</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3.010.349</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{192}" paraid="887170639" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{196}" paraid="91045730" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">12.752.043=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">34</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-34</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=12.752.043</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{210}" paraid="229089879" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{214}" paraid="1860574762" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Επίσης για την χρυσή τομή φ ισχύουν οι σχέσεις:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{220}" paraid="1818414001" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-style: italic; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{224}" paraid="1173421620" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-10</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=89-55·φ=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-11</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-12</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-8</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-9</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{248}" paraid="739385009" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cea50b40-4bcf-4c0f-b6b5-eb36d4e86a69}{252}" paraid="1136558902" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-9</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=34</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ-55=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-10</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-11</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-8</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{25}" paraid="266745892" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{29}" paraid="173384720" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-8</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=34-21</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-9</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-10</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-6</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-7</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{57}" paraid="1617242" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{61}" paraid="532652492" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=13</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ-21=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-8</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-9</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-6</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{89}" paraid="110134455" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{93}" paraid="191005983" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-6</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=13-8</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-8</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{121}" paraid="1984187893" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{125}" paraid="243773603" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=5</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ-8=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-6</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=5</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-13=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(2+</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-13=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+1</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-13=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">[(</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+1</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-2]</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{201}" paraid="1173026932" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{205}" paraid="1416215666" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=5-3</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-6</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{233}" paraid="549647898" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{3c252bd2-0378-443a-8a5f-d2757bbe651d}{237}" paraid="1490786721" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ-3=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{10}" paraid="1074552994" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{14}" paraid="701633055" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2-φ=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{34}" paraid="1647372967" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{38}" paraid="884615114" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ-1=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-2=(2-φ)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{64}" paraid="607636576" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{68}" paraid="292415079" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">0</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1=0+1=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{88}" paraid="318471797" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{92}" paraid="1910700674" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ=φ+0=1+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{104}" paraid="685796592" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{108}" paraid="593371375" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ+1=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+2</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{122}" paraid="1859954912" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{126}" paraid="1019113646" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+1=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ=2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-1=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{158}" paraid="1951323633" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{162}" paraid="602371453" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+2=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">6</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{190}" paraid="299000149" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{194}" paraid="353890447" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=5</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+3=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=(</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-2</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{226}" paraid="1519118803" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{e0b7f24e-d80d-444c-8158-c1b5f65d1f99}{230}" paraid="455857090" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">6</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=8</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+5=4</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+1=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{3}" paraid="2036602736" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{7}" paraid="434549515" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">7</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=13</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+8=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">6</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{27}" paraid="953211307" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{31}" paraid="363360148" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-8bbd73c6-7fff-ee0a-cfbd-2724d5650a1b"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=21·φ+13=7·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">1=φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=3·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+5·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+2·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=8·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+5·φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{177}" paraid="65692930" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{181}" paraid="529086227" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">10</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=55</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+34=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">9</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">8</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{201}" paraid="816454410" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{205}" paraid="1218263264" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">11</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=89</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+55=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">10</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">9</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{225}" paraid="1030832652" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{229}" paraid="604141830" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">12</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=144</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+89=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">11</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">10</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{249}" paraid="452695034" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{15c225be-7b87-4bc9-ad3e-bd9f920b2fce}{253}" paraid="152510118" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">13</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=233</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+144</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{12}" paraid="195752783" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{16}" paraid="938857453" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">14</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=377</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+233</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{30}" paraid="1533672259" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{34}" paraid="739827125" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">15</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=610</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+377</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{48}" paraid="2088189427" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{52}" paraid="1149435985" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">16</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=987</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+610</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{66}" paraid="1256672292" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{70}" paraid="1634105334" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">17</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1.597</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+987=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">18</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">16</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{90}" paraid="385447228" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{94}" paraid="328487521" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">18</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2.584</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+1.597</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{108}" paraid="1438776781" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{112}" paraid="1319876663" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">19</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=4.181</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+2.584</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{126}" paraid="1135441345" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{130}" paraid="20959586" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">20</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=6.765</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">·</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+4.181</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{144}" paraid="316468135" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{148}" paraid="93464779" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Αριθμητική τιμή τ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">ης χρυσής τομής φ</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{156}" paraid="182867359" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{160}" paraid="209469575" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Η αριθμητική τιμή τ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">ης χρυσής τομής φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> στα πρώτα ενενήντα δεκαδικά ψηφία του είναι:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{170}" paraid="1875434334" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{174}" paraid="1608155394" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">....</span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{184}" paraid="1695522056" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{188}" paraid="853960497" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">Προσεγγίσεις</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> της χρυσής τομής φ</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{196}" paraid="1234431861" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{200}" paraid="1522935656" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Οι 27 αριθμητικές προσέγγισεις της χρυσής τομής φ είναι: </span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{210}" paraid="1940811120" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{214}" paraid="1977929693" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1) φ≃13</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">8=1,6</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{228}" paraid="1183699559" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{232}" paraid="604557888" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2) φ≃144</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">89=1,61</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{246}" paraid="1384062387" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{d9686e1c-be98-48e0-b40e-b98755c87ce1}{250}" paraid="612623432" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3) φ≃89</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">55=1,618</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{9}" paraid="2087978146" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{13}" paraid="1236543978" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">4) φ≃377</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">233=1,6180</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{27}" paraid="2081820239" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{31}" paraid="1592767835" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5) φ≃521</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">322=1,6180</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{45}" paraid="808701710" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{49}" paraid="1232683499" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6) φ≃843</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">521=1,6180</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{63}" paraid="628451812" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{67}" paraid="1809529871" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">7) φ≃1.597</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">987=1,61803</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{81}" paraid="602694759" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{85}" paraid="1024745529" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">8) φ≃1.364</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">843=1,61803</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{99}" paraid="709304067" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{103}" paraid="712065426" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">9) φ≃4.181</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2.584=1,61803</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{117}" paraid="64587103" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{121}" paraid="717296397" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">10) φ≃5.778</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3.571=1,61803</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{135}" paraid="910407396" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{139}" paraid="845817623" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">11) φ≃2.207</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1.364=1,618033</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{153}" paraid="647220317" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{157}" paraid="762468203" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">12) φ≃3.571</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2.207=1,618033</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{171}" paraid="258015242" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{175}" paraid="567443495" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">13) φ≃2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">856</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1.233</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1,618033</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{193}" paraid="710518889" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{197}" paraid="2084117005" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">14) φ≃9.349</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5.778=1,6180339</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{211}" paraid="198892895" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{215}" paraid="609512434" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">15) φ≃10.946</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6.765=1,6180339</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{229}" paraid="2026213067" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{233}" paraid="1849719022" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">16) φ≃(5.778)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">18</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1,6180339</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{251}" paraid="666031680" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{cfa47ce9-ea67-4218-ade9-9df2d761c787}{255}" paraid="16962793" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">17) φ≃(3.571)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">17</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1,61803398</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{18}" paraid="1008697250" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{22}" paraid="517829004" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">18) φ≃(9.349)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/19</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1,61803398</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{36}" paraid="1946271202" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{40}" paraid="511868010" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">19) φ≃46.368</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">28.657=1,618033988</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{54}" paraid="2116115721" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{58}" paraid="879586339" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">20) φ≃121.393</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">75.025=1,618033988</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{72}" paraid="857233868" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{76}" paraid="557447546" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">21) φ≃317.811</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">196.418=1,6180339887</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{90}" paraid="1545520115" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{94}" paraid="572857061" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">22) φ≃(1.860.498)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">30</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,618033988749...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{112}" paraid="735904805" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{116}" paraid="1753981893" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">23) φ≃(2.537.720.636)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">45</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,618033988749894...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{134}" paraid="1188241336" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{138}" paraid="319831347" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">24) φ≃(3.461.452.808.002)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">60</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,618033988749894...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{156}" paraid="874224336" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{160}" paraid="1461754660" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">25) φ≃(4.721.424.167.835.364)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">75</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,618033988749894...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{178}" paraid="935569298" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{182}" paraid="1052397014" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">26) φ≃(6.440.026.026.380.244.498)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">90</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1,618033988749894...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{198}" paraid="250811017" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{202}" paraid="547568726" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">27) φ≃7.778.742.049</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">4.807.526.976=</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,6180339887498948482...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{216}" paraid="1524435985" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{220}" paraid="308228972" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Επίσης η χρυσή τομή φ μπορεί να προσεγγιστεί από τις ανισότητες:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{226}" paraid="1542396290" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{230}" paraid="1011585213" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">8/5<φ<81/50</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{234}" paraid="916066858" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{238}" paraid="1936057703" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Συζυγής Φ της χρυσής τομής</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{244}" paraid="102844170" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{7b61da95-ec6d-45c7-b99f-165b60c65352}{248}" paraid="245965348" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> Ο συζυγής Φ της χρυσής τομής φ </span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">ισούται με τις σχέσεις</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">:</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{3}" paraid="1664429633" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{7}" paraid="1188561386" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Φ=1/φ </span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{13}" paraid="360149131" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{17}" paraid="1547764340" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Φ=φ-1</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{23}" paraid="1719366443" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{27}" paraid="1373665011" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Φ=φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-2</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{37}" paraid="1893373072" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{41}" paraid="778566266" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Φ=(2-φ)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{49}" paraid="1833748178" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{53}" paraid="52704667" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Ο συζυγής Φ της χρυσής τομής φ έχει τιμή:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{59}" paraid="713393706" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{63}" paraid="1490182403" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Φ=(√5-1)</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2=2</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(√5+1)</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{77}" paraid="1865895598" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{81}" paraid="1239546740" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Η αριθμητική τιμή του Φ στα πρώτα </span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">ενενήντα</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> δεκαδικά ψηφία του είναι:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{91}" paraid="883168405" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{95}" paraid="969060492" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=0,</span><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720...</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">....</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{107}" paraid="1448123242" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{111}" paraid="1758525469" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Για το συζυγή Φ της χρυσής τομής φ ισχύουν:</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{117}" paraid="83530362" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{121}" paraid="1784068847" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">+</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">2</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">∙</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">Φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{141}" paraid="1600394282" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><p class="Paragraph SCXW60264244 BCX0" paraeid="{37bab28b-df9d-4646-8e9f-5cc8a1c5cb74}{49}" paraid="555327882" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; font-size: 12px; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span class="EOP SCXW60264244 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-family: verdana; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"></span></p><div class="OutlineElement Ltr BCX0 SCXW210773143" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{145}" paraid="972481695" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; font-size: 12px; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Φ</span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">+5</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">∙</span><span class="NormalTextRun SCXW210773143 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">Φ</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW210773143 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW210773143 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2</span><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{145}" paraid="972481695" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; font-size: 12px; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-family: verdana; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"><br /></span></p><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{167}" paraid="1083559271" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1.3 Σταθερά e</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{173}" paraid="224954825" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{177}" paraid="1004075948" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Εισαγωγή</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{183}" paraid="944109520" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{187}" paraid="1668467877" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-42cdfce2-7fff-ad6b-bfe1-2fd39a191ff9"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Ο αριθμός e είναι σημαντική μαθηματική σταθερά,η οποία αποτελεί τη βάση του φυσικού λογαρίθμου. Είναι το όριο της ακολουθίας (1+1/n)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">n</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> όσο το n πλησιάζει το άπειρο,μια έκφραση που προκύπτει από την μελέτη των σύνθετων τόκων. Αναφέρεται επίσης ως αριθμός Euler και μερικές φορές είναι γνωστή ως σταθερά του Napier. Όπως και ο αριθμός π,έτσι και ο αριθμός e είναι ένας άρρητος δηλαδή δεν είναι λόγος ακεραίων και υπερβατικός αριθμός δηλαδή δεν είναι ρίζα κάθε μη-μηδενικού πολυώνυμου με ρητούς συντελεστές.</span></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEyMzowtYQo2Y6g12RPtHi0H2Xt02bHOX-y3GAd_3U6DbVyXoBBlwUg97gT2CxOahTnBhGvQHJDSAwjbIIxoe4iPlarvir94D63zzxK28r0Xk6aOu-9d9BxOzQbBj3o7e-Q9hasMZQ6rM/s357/%25CE%25B1%25CF%2581%25CE%25B9%25CE%25B8%25CE%25BC%25CF%258C%25CF%2582+Euler.gif" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="218" data-original-width="357" height="244" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEyMzowtYQo2Y6g12RPtHi0H2Xt02bHOX-y3GAd_3U6DbVyXoBBlwUg97gT2CxOahTnBhGvQHJDSAwjbIIxoe4iPlarvir94D63zzxK28r0Xk6aOu-9d9BxOzQbBj3o7e-Q9hasMZQ6rM/w400-h244/%25CE%25B1%25CF%2581%25CE%25B9%25CE%25B8%25CE%25BC%25CF%258C%25CF%2582+Euler.gif" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-family: verdana; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Η τιμή του (1+1/n)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-family: verdana; font-size: 9.5pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">n</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-family: verdana; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> πλησιάζει το </span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-family: verdana; font-size: 12pt; font-style: italic; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">e</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-family: verdana; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> καθώς το n γίνεται όλο και μεγαλύτερο.</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":2,"335551620":2,"335559739":160,"335559740":259}" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #002060; font-family: verdana; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></td></tr></tbody></table><p></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{3}" paraid="683914081" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> </span></span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Ο αριθμός e έχει εξέχουσα σημασία στα μαθηματικά,παράλληλα με τα 0,1,π και i. Και οι πέντε από αυτούς τους αριθμούς παίζουν σημαντικούς και επαναλαμβανόμενους ρόλους στα μαθηματικά και αυτές οι πέντε σταθερές εμφανίζονται σε μια διατύπωση της ταυτότητας του Euler. Ο αριθμός του Euler έχει πολλές πρακτικές χρήσεις,ιδιαίτερα σε μαθηματικά υψηλότερου επιπέδου όπως ο λογισμός,οι διαφορικές εξισώσεις,η τριγωνομετρία,η σύνθετη ανάλυση,η στατιστική κ.α. Από την ταυτότητα του Euler μπορεί να προκύψει η παρακάτω σχέση της μαθηματικής σταθεράς e: </span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{55}" paraid="343259041" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{59}" paraid="1134022546" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">e=i</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2i/π</span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{67}" paraid="1902678367" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{71}" paraid="33837048" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Ιστορία</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{77}" paraid="733161573" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{81}" paraid="2146031714" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> </span></span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Η ιστορία της μαθηματικής σταθεράς e ξεκινά από τον John Napier (1.550-1.617) ο οποίος καθόρισε λογάριθμους μέσω μιας διαδικασίας που ονομάζεται δυναμική αναλογία. Ωστόσο,αυτό δεν περιείχε την ίδια τη σταθερά,αλλά απλώς μια λίστα λογαρίθμων που υπολογίστηκε από τη σταθερά. Υποτίθεται ότι ο πίνακας γράφτηκε από τον William Oughtred. Η πρώτη γνωστή χρήση της σταθεράς,που αντιπροσωπεύεται από το γράμμα β,ήταν η αλληλογραφία από τον Gottfried Leibniz προς τον Christiaan Huygens το 1.690 και το 1.691. Όμως η ανακάλυψη της ίδιας της σταθεράς e πιστώνεται στον Jacob Bernoulli το 1.683</span><span style="background-color: transparent; font-family: Verdana; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">όταν μελετούσε τους σύνθετους τόκους. Ο Leonhard Euler εισήγαγε το γράμμα e ως βάση για τους φυσικούς λογάριθμους,γράφοντας σε μια επιστολή προς τον Christian Goldbach την 25 Νοεμβρίου 1.731. Ο Leonhard Euler (1.707-1.783) που έδωσε στη σταθερά το γράμμα του την ονομασία e και ανακάλυψε πολλά από αυτές τις αξιοσημείωτες ιδιότητες. </span></p><div><br /></div></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">Αριθμητική τιμή </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;"> Η αριθμητική τιμή της μαθηματικής σταθεράς e στα πρώτα ενενήντα δεκαδικά ψηφία του είναι: </span></p><span id="docs-internal-guid-00f8d94e-7fff-d77a-8a53-07600f12bce3"><p dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></p><p dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e=2,71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217....</span></p><p dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p></span><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">Προσεγγίσεις </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{105}" paraid="1657035185" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-e5198e11-7fff-18b8-1735-288e405910e5"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Οι 26 αριθμητικές προσέγγισεις της σταθεράς e είναι: </span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{169}" paraid="424865465" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{173}" paraid="325023120" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1) e≃19</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">7=2,71</span><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">................</span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{185}" paraid="40227335" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{189}" paraid="1827435535" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2) e≃87</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">32=2,718</span><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">................</span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{201}" paraid="2130801501" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{205}" paraid="1532130222" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3) e≃193</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">71=2,718</span><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">................</span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{217}" paraid="114683600" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{221}" paraid="1777587244" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">4) e≃1.264</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">465=2,7182.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{231}" paraid="2145717712" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{235}" paraid="1864796093" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5) e≃878</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">323=2,7182.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{245}" paraid="670097487" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{78af0133-1186-428f-aaeb-8b407e59e49d}{249}" paraid="1045249249" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6) e≃(5</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">93</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">π</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">6</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2,71828.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{16}" paraid="1330593797" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{20}" paraid="288610621" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">7) e≃3</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+4</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">100</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2,71828.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{42}" paraid="672284169" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{46}" paraid="1302418015" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">8) e≃(355</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">113)-(69/163)=2,71828.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{56}" paraid="1464402230" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{60}" paraid="865218280" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">9</span><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) e≃2.721</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1.001=</span><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2,718281</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{76}" paraid="274758030" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{80}" paraid="1822643842" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">10) e≃(1/7)-[8</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">ln(4/5)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">ln2]=</span><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2,718281</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{98}" paraid="1378929771" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{102}" paraid="632839874" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">11</span><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) e≃3-(5</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">63)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2,718281.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{118}" paraid="860427832" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{122}" paraid="1724714058" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">12</span><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) e≃163</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">32</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">163</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2,718281.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{138}" paraid="1850550700" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{142}" paraid="788871023" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">13) e≃23.225</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">8.544=2,7182818.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{152}" paraid="1641048032" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{156}" paraid="1338732238" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">14</span><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">) e≃2+(54</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+41</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">80</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2,7182818.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{180}" paraid="1821013239" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{184}" paraid="816340316" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">15) e≃(1+5</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/5</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3=2,7182818.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{202}" paraid="1648012399" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{206}" paraid="1678149066" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">16) e≃(1+1/80</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)∙(1+1/2+1/3+1/4+1/5+1/6+1/7+1/8)=2,7182818.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{216}" paraid="1846264572" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{220}" paraid="484781384" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">17) e≃(1+9</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-9</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">387.420.489</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2,71828182.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{234}" paraid="1458942014" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{238}" paraid="1380048019" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">18) e≃49.171</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">18.089=2,718281828.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{248}" paraid="1627896347" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f0b51d82-b399-40b4-a42e-49c7dd08b5b3}{252}" paraid="1084330936" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">19) e≃271.801</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">99.990=2,718281828.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{7}" paraid="47845856" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{11}" paraid="749659462" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">20) e≃517.656</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">190.435=2,7182818284.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{21}" paraid="534534421" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{25}" paraid="1955071642" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">21) e≃[150-(87</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+12</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">83</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">]</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/5</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2,7182818284.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{51}" paraid="453588287" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{55}" paraid="1689780968" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">22) e≃(37/613)∙[45+(35/991)]=2,7182818284.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{61}" paraid="1439838631" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{65}" paraid="1640946273" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">23) e≃[8</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(9.112.774</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/4</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-52)]=2,71828182845.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{79}" paraid="909096025" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9pt; font-variant-ligatures: none; line-height: 15.1083px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Arial, Arial_EmbeddedFont, Arial_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9pt; line-height: 15.1083px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{83}" paraid="270562613" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">24) e≃4-[(300</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-100</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-1.291</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+9</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">91</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">]=2,718281828459.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{113}" paraid="515536325" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{117}" paraid="1777541956" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">25) e≃[1.097-(55</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+311</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-11</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">68</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">]</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/7</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2,718281828459045</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{149}" paraid="64937881" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{153}" paraid="931324393" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">26) e≃</span><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">848.456.353</span><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">312.129.649=2,71828182845904523.............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{163}" paraid="917464962" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{167}" paraid="1193888402" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Επίσης η σταθερά e μπορεί να προσεγγιστεί από τις ανισότητες:</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{173}" paraid="1012925956" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{177}" paraid="1007848085" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2+7/10<e<2+3/4</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{181}" paraid="1163883568" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{185}" paraid="315361099" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1.4</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Φανταστικός αριθμός i</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{193}" paraid="1186937177" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{197}" paraid="1810546338" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Εισαγωγή</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{203}" paraid="1769299902" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{207}" paraid="1468680548" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">H φανταστική μονάδα i είναι μια λύση στην τετραγωνική εξίσωση x</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">+1=0. Αν και δεν υπάρχει πραγματικός αριθμός με αυτήν την ιδιότητα,μπορεί να χρησιμοποιηθεί για να επεκτείνει τους πραγματικούς αριθμούς σε αυτούς που ονομάζονται σύνθετοι αριθμοί. Παρά το παραπλανητικό τους όνομα,οι φανταστικοί αριθμοί είναι όχι μόνο υπαρκτοί αλλά και πολύ χρήσιμοι,με εφαρμογή στον ηλεκτρισμό,στην επεξεργασία σημάτων και σε πολλές άλλες εφαρμογές. Χρησιμοποιούνται ευρύτατα στην ηλεκτρονική,για την αναπαράσταση εναλλασσόμενων ρευμάτων,στην κυματική και γενικά στη μελέτη των περιοδικών φαινομένων. </span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{217}" paraid="2119741359" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{221}" paraid="1551733069" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Ιστορία</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{227}" paraid="1619825553" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span><span color="windowtext" style="background-color: transparent; font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> </span></span></span><span color="windowtext" style="background-color: transparent;"> </span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><span id="docs-internal-guid-6e95c0d1-7fff-972c-6cdb-38d642561c3c"><p dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Αν και ο Έλληνας μαθηματικός και μηχανικός Ήρωας της Αλεξάνδρειας είναι ο πρώτος που έχει συλλάβει φανταστικούς αριθμούς,ήταν ο Rafael Bombelli που έθεσε για πρώτη φορά τους κανόνες για τον πολλαπλασιασμό των πολύπλοκων αριθμών το 1.572. Η ιδέα εμφανίστηκε σε έντυπη μορφή νωρίτερα,όπως στην εργασία του Gerolamo Cardano. Εκείνη την εποχή,οι φανταστικοί αριθμοί και οι αρνητικοί αριθμοί ήταν ελάχιστα κατανοητοί και θεωρούνταν από μερικούς ως φανταστικούς ή άχρηστους όπως ήταν το μηδέν κάποτε. Πολλοί άλλοι μαθηματικοί καθυστέρησαν να υιοθετήσουν τη χρήση φανταστικών αριθμών,συμπεριλαμβανομένου του René Descartes. Η χρήση φανταστικών αριθμών δεν έγινε ευρέως αποδεκτή μέχρι το έργο των Leonhard Euler (1.707–1.783) και Carl Friedrich Gauss (1.777–1.855). Η γεωμετρική σημασία των σύνθετων αριθμών ως σημεία σε ένα επίπεδο περιγράφεται για πρώτη φορά από τον Caspar Wessel (1.745-1.818). Το 1.843,ο William Rowan Hamilton επέκτεινε την ιδέα ενός άξονα φανταστικών αριθμών στο αεροπλάνο σε έναν τετραδιάστατο χώρο τεταρτημορίων,όπου τρεις από τις διαστάσεις είναι ανάλογες με τους φανταστικούς αριθμούς στο περίπλοκο πεδίο. </span></p></span></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{237}" paraid="862542675" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{241}" paraid="929118062" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Σχέσεις</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{247}" paraid="95020972" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{f7335749-9959-4f12-987a-449fceed0da4}{251}" paraid="238548636" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> H φανταστική μονάδα i έχει την ιδιότητα:</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{2}" paraid="1723700130" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{6}" paraid="77142701" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">i</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=−1</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{14}" paraid="2046526253" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{18}" paraid="197503764" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Η τετραγωνική ρίζα του i είναι:</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{24}" paraid="332541837" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{28}" paraid="452648145" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">√i=±(i+1)</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{38}" paraid="1887497383" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{42}" paraid="1947871873" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> Για την φανταστική μονάδα i ισχύει:</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{48}" paraid="1302404454" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{52}" paraid="848082782" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">i</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4n</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{60}" paraid="759325228" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{64}" paraid="158988580" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">i</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4n+1</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=i</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{72}" paraid="183583904" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{76}" paraid="1321583256" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">i</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4n+2</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=-1</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{84}" paraid="834846706" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{88}" paraid="187569053" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">i</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4n+3</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=-i</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{96}" paraid="1684100913" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #202122; font-size: 10.5pt; font-variant-ligatures: none; line-height: 18.3458px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #202122; font-size: 10.5pt; line-height: 18.3458px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">το η είναι οποιοσδήποτε ακέραιος.Επίσης ισχύει: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">cosi=(e+1/e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2∙e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{100}" paraid="1297493730" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-dc4f2b4a-7fff-c9bc-c014-d32a9e86a41d"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">sini=(e-1/e)∙i</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2=(e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">-1)∙i</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">2∙e </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{168}" paraid="67848538" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{172}" paraid="820567039" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1.5 Άλλοι αριθμοί</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{178}" paraid="583446402" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">Σταθερά του Gelfond </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: left; vertical-align: baseline; white-space: pre-wrap;"> Η σταθερά του Gelfond,στα μαθηματικά είναι ο αριθμός e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: left; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: left; vertical-align: baseline; white-space: pre-wrap;">,που είναι ο αριθμός e υψωμένος στη δύναμη π. Όπως και τα e και π,αυτή η σταθερά είναι ένας υπερβατικός αριθμός. Πήρε το όνομα του από τον Σοβιετικό μαθηματικό Aleksandr Gelfond. H σταθερά του Gelfond e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: left; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: left; vertical-align: baseline; white-space: pre-wrap;"> ξεχωρίστηκε στο 7ο πρόβλημα του Hilbert ως παράδειγμα αριθμών των οποίων η υπέρβαση ήταν ένα ανοιχτό πρόβλημα. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-i</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=(-1)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-i</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Η αριθμιτική τιμή της σταθεράς του Gelfond είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃23,14069263277926900572.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Οι 17 αριθμητικές προσέγγισεις της σταθεράς του Gelfond είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃2∙(4∙π-1)=23,1..... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃23+π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1-e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=23,1....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃20+π=23,14..... με ακρίβεια σφάλματος 0,005% </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃162</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7=23,14..... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">∙[3+(4+√5)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">])</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=23,140......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃302∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">41=23,140...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃3.241∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">440=23,1406...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃[29</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">42+(9.507)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]=23,14069...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">9) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃30+(1+√2)-345</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7=23,140692...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃ln3+(159/5)∙ln2=23,14069263...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">11) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃7∙π+1+(-e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+28∙e+189</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">634∙e)=23,1406926327...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">12) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃6.112.351∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">829.816=23,140692632779...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">13) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃7∙π+(365.455</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">317.913)=23,140692632779...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">14) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃17+√3+(172))</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+ln(ln9)=23,1406926327792...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">15) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃20+π+1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">[1.111+1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(11+1/√2)]=23,1406926327792...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">16) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃(421∙π-133∙φ-316)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(-176∙π+539∙φ-285)=23,14069263277926......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{182}" paraid="554051794" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-bd5d1d49-7fff-44f5-3758-393959e82b7c"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">17) e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃(-381∙π+363∙φ+469∙e+127)</span><span style="background-color: transparent; font-family: Verdana; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">/</span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">(44∙π+11∙φ+88∙e-361)</span></span></p><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{182}" paraid="554051794" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p class="Paragraph SCXW99266595 BCX0" paraeid="{d9d8bd5b-37e3-4403-ad96-fd439e953480}{182}" paraid="554051794" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span color="windowtext" style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;">=23,140692632779260057......... </span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{ba225893-a4ec-48f3-9d06-b1a670991fe0}{212}" paraid="2006243190" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{ba225893-a4ec-48f3-9d06-b1a670991fe0}{216}" paraid="2138142592" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">Αριθμός </span><span class="SpellingError SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-image: url("data:image/gif;base64,R0lGODlhBQAEAJECAP////8AAAAAAAAAACH5BAEAAAIALAAAAAAFAAQAAAIIlGAXCCHrTCgAOw=="); background-position: 0% 100%; background-repeat: repeat-x; border-bottom: 1px solid transparent; margin: 0px; padding: 0px; user-select: text;">i</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="SpellingError SpellingErrorSuperscript Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-image: url("data:image/gif;base64,R0lGODlhBQAEAJECAP////8AAAAAAAAAACH5BAEAAAIALAAAAAAFAAQAAAIIlGAXCCHrTCgAOw=="); background-position: 0% 100%; background-repeat: repeat-x; border-bottom: 1px solid transparent; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">i</span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{ba225893-a4ec-48f3-9d06-b1a670991fe0}{224}" paraid="215758242" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Ο αριθμός i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">i </span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">ισούται:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-π/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Η δεκαδική επέκταση του i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">i </span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p class="Paragraph SCXW99266595 BCX0" paraeid="{ba225893-a4ec-48f3-9d06-b1a670991fe0}{228}" paraid="1113697693" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-52163982-7fff-99e5-e8d1-ef2d334bcecf"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">i</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">≃0,20787957635076190854...... </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{e8519ad6-3b7a-4559-a2ba-54fb14b4c4f6}{43}" paraid="259830578" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">Αριθμός π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Η δεκαδική επέκταση του π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃22,45915777183610454734......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Δεν είναι γνωστό εάν αυτός ο αριθμός είναι υπερβατικός. Για την σταθερά του Gelfond e</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">π </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">και τον αριθμό π</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">e </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">ισχύει: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃2=2,000893…...... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">Αριθμός e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">-π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Η δεκαδική επέκταση του e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p aria-level="3" class="Paragraph SCXW99266595 BCX0" paraeid="{e8519ad6-3b7a-4559-a2ba-54fb14b4c4f6}{47}" paraid="79714995" role="heading" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: #1f3763; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-ed5ac687-7fff-739a-01d8-97a1ff68877c"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃0,68153491441822353230........ </span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{e8519ad6-3b7a-4559-a2ba-54fb14b4c4f6}{207}" paraid="2119386633" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{e8519ad6-3b7a-4559-a2ba-54fb14b4c4f6}{211}" paraid="149711874" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">Άλλοι αριθμοί</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{e8519ad6-3b7a-4559-a2ba-54fb14b4c4f6}{217}" paraid="712347934" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; font-weight: bold; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{e8519ad6-3b7a-4559-a2ba-54fb14b4c4f6}{221}" paraid="1671392273" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">φ</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃2,178457567938..........</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{e8519ad6-3b7a-4559-a2ba-54fb14b4c4f6}{231}" paraid="237443181" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{e8519ad6-3b7a-4559-a2ba-54fb14b4c4f6}{235}" paraid="120187323" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">π</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃4,53475716116............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{e8519ad6-3b7a-4559-a2ba-54fb14b4c4f6}{245}" paraid="1332168933" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{e8519ad6-3b7a-4559-a2ba-54fb14b4c4f6}{249}" paraid="154857047" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">e</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃3,69902532658..........</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{4}" paraid="1198957534" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; font-weight: bold; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{8}" paraid="1646389326" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">π</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">φ</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃6,37951853648..........</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{18}" paraid="350070627" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{22}" paraid="1796793972" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">e</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">φ</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃5,04316564336...........</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{32}" paraid="158163172" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{36}" paraid="1226223896" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">φ</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙φ</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">π</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃9,8787760564777..........</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{50}" paraid="1973748486" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{54}" paraid="396016598" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">e</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙e</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">π</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃85,59800812326............</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{68}" paraid="2126680253" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{72}" paraid="1153443373" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">π</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙π</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">e</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">≃101,84682653935</span><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">...........</span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{88}" paraid="959184547" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW99266595 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><p class="Paragraph SCXW210773143 BCX0" paraeid="{0b31503b-a64b-4be6-88ad-cbd15e3e6120}{145}" paraid="972481695" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; font-size: 12px; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span class="EOP SCXW210773143 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-family: verdana; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"></span></p><div class="OutlineElement Ltr BCX0 SCXW99266595" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{92}" paraid="1831635612" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; font-size: 12px; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">π</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙e</span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW99266595 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">π</span></span><span class="TextRun SCXW99266595 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃104,93742163059...........</span><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p><p class="Paragraph SCXW99266595 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{92}" paraid="1831635612" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; font-size: 12px; margin: 0px; overflow-wrap: break-word; padding: 0px; user-select: text; vertical-align: baseline;"><span class="EOP SCXW99266595 BCX0" data-ccp-props="{"201341983":0,"335559739":160,"335559740":259}" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-family: verdana; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"><br /></span></p><div class="OutlineElement Ltr BCX0 SCXW240281116" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW240281116 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{112}" paraid="923154527" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW240281116 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; font-weight: bold; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2.Ακριβείς σχέσεις </span><span class="TextRun SCXW240281116 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; font-weight: bold; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">μεταξύ μαθηματικών σταθερών</span><span class="EOP SCXW240281116 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW240281116" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW240281116 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{120}" paraid="1278420494" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW240281116 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW240281116 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW240281116 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW240281116" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">2.1 Ακριβείς σχέσεις μεταξύ φ και π </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Οι 47 ακριβείς σχέσεις μεταξύ της χρυσής τομής φ και της σταθεράς π είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) φ=2∙cos(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) φ=2∙sin(3∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) φ=1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2∙cos(2π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4) φ=1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2∙sin(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) φ=-2∙cos(4∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6) φ=1-2∙cos(3∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7) φ=(1/2)∙sec(2∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8) φ=(1/2)∙csc(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">9) φ=sin(3∙π/10)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">sin(π/6) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) φ=sin(π/6)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">sin(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">11) φ=sin(2∙π/5)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">sin(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">12) φ=sin(5π/6)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">sin(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">13) φ=sin(7∙π/10)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">sin(π/6) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">14) (3-φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">15) (φ∙√5)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">16) cos(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1+φ)+cos(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">φ)=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">17) φ=[π+(5∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2∙π </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">18) (2-φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(2∙π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">19) [2-(1/φ)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(3∙π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">20) [2+(1/φ)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">21) (2+φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">22) (2-φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">23) (2-φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">24) (2+φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(3∙π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">25) (2+φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(2∙π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">26) [2+(2+φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">27) [2+(2+φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">28) [2+(2-φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(3∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">29) [2+(2-φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">30) [2-(2-φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(3∙π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">31) [2-(2-φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(7∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">32) [2-(2+φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(2∙π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">33) [2-(2+φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(9∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">34) [2+(2+φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(9∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">35) [2+(2+φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(2∙π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">36) [2+(2-φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(7∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">37) [2+(2-φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(3∙π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">38) [2-(2-φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">39) [2-(2-φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(3∙π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">40) [2-(2+φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">41) [2-(2+φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙sin(π/20) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">43) φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+(3∙φ∙√5)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=4∙cos(π/15) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">44) (φ∙√5)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙cos(π/10) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">45) φ+(3∙φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">∙√5)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=4∙cos(2∙π/15) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">46) -φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+(3∙φ∙√5)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=4∙cos(4∙π/15) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p class="Paragraph SCXW240281116 BCX0" paraeid="{d5750719-fa5e-4cb4-badc-0cf30c8590b6}{124}" paraid="1582074805" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-2c5be655-7fff-1473-3c94-e65622bf393d"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">47) -φ+(3∙φ</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">∙√5)</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">=4∙cos(7∙π/15) </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW240281116" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW240281116 BCX0" paraeid="{f5011991-c6ed-462a-b64d-ac636f704f5b}{242}" paraid="1457361880" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW240281116 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW240281116 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW240281116 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW240281116" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">2.2 Ακριβείς σχέσεις μεταξύ φ και e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Oι 11 ακριβείς σχέσεις μεταξύ φ και e είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) e=(2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">φ-1)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2/ln(5)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) φ=(1+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) φ=</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">(1/2)ln(φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">φ-1)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+1=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) φ=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln(-1)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-ln(-1)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">(1/2)ln(φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">φ-1)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln(-1)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+2∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-ln(-1)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">(1/2)ln(φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">φ-1)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln(-1)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-ln(-1)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">9) φ=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">(1/2)ln(φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">φ-1)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">11) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 21pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1+φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 21pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1+φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 21pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 21pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">2.3 Ακριβείς σχέσεις μεταξύ π και e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Οι 8 ακριβείς σχέσεις μεταξύ της σταθεράς π και της σταθεράς e είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=4∙cos(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=4∙sin(3∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=1-4∙cos(3∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=sec(2∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=csc(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6) 2∙sin(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5)=[3-</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">½</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7) cos[π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1+</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2)]+cos[2∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)]=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">={[π+(5∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π}-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">2.4 Ακριβείς σχέσεις μεταξύ π και i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Οι 3 ακριβείς σχέσεις της σταθεράς π και της φανταστικής μονάδας i είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) π=2∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) π=2∙i∙log(1-i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1+i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) π=-i∙ln(-1) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">2.5 Ακριβείς σχέσεις μεταξύ φ και i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> <span id="docs-internal-guid-9b5e6419-7fff-2e8b-487b-be32b7f5b342"><span style="background-color: transparent; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Οι 12 ακριβείς σχέσεις μεταξύ της χρυσής τομής φ και της φανταστικής μονάδας i είναι: </span></span></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+i∙φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=(1+2∙i)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+i∙φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-3/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2∙[1+(i/2)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) 2∙sin(i∙lnφ)=i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4) sin</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(i∙lnφ)=-1/4 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) φ=[ln(cosφ+i∙sinφ)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6) 2∙sin(i∙lnφ)=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-lnφ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">lnφ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7) 2∙sin(i∙lnφ)=-i∙[(1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">φ)-φ] </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8) φ=2∙cos(2∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">9) φ=2∙sin(3∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) φ=1-2∙cos(6∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">11) φ=(1/2)∙sec(4∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">12) φ=(1/2)∙csc(lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">13) 2∙sin(2∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i)=(3-φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">14) cos(2∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">i∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1+φ)+cos(2∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">i∙φ)=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">2.6 Ακριβείς σχέσεις μεταξύ e και i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;">Οι 11 ακριβείς σχέσεις μεταξύ της της σταθεράς e και της φανταστικής μονάδας i είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) cosi=(e+1)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2∙e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) sini=(e-1)∙i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2∙e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-1=2∙i∙e∙sini </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4) sini=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2∙i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-e=2∙i∙sini </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=4∙cos(2∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=4∙sin(3∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=1-4∙cos(6∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">9) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=sec(4∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=csc(lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i)-1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">11) 2∙sin(2∙lni</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙i)=[3-</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ln5/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">2.7 Ακριβείς σχέσεις π,φ και i </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> <span id="docs-internal-guid-610fdcef-7fff-55bf-9db9-2074aa7b8a18"><span style="background-color: transparent; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Οι 4 ακριβείς σχέσεις μεταξύ της σταθεράς π,της χρυσής τομής φ και της της φανταστικής μονάδας i είναι: </span></span> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) sin[(π/2)-i∙lnφ]=√5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) i∙π=ln(φ)+ln(1-φ) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) π=-5∙i∙log{(1/2)∙[φ+i∙(4-φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]} </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4) φ=</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">φ-1)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5ln(5)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">∙</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">φ-1)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-2iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5ln(5)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">2.8 Ακριβείς σχέσεις μεταξύ φ,e και i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Οι 3 ακριβείς σχέσεις μεταξύ της χρυσής τομής φ,της σταθεράς e και της της φανταστικής μονάδας i είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iφ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=cosφ+i∙sinφ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) φ=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2lni</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-2lni</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iφ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=cos(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2lni</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-2lni</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)+i∙sin(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2lni</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-2lni</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">2.9 Ακριβείς σχέσεις φ,π και e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Οι 3 ακριβείς σχέσεις μεταξύ της σταθεράς π,της χρυσής τομής φ και της σταθεράς e είναι:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) 2∙cos(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">(1/2)ln(φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">φ-1)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) 2∙cos(π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5)=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-[ln(φ)+ln(1-φ)]</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p class="Paragraph SCXW240281116 BCX0" paraeid="{f5011991-c6ed-462a-b64d-ac636f704f5b}{246}" paraid="638825355" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-c85b409b-7fff-ee71-7070-92eae200c5ce"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) φ=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">{ln[2cos(π/5)]+ln(2φ-1)}</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-iπ{ln[2cos(π/5)]+ln(φ-1)}</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p></div><div class="OutlineElement Ltr BCX0 SCXW240281116" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW240281116 BCX0" paraeid="{321b5d00-2bdb-49be-813f-99f04d2d0ddb}{4}" paraid="1734408639" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW240281116 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW240281116 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW240281116 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW240281116" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">2.10 Ακριβείς σχέσεις μεταξύ π,e και i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Θα παρουσιάσουμε 10 ακριβείς σχέσεις μεταξύ π,e και i. </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Στα μαθηματικά,η ταυτότητα του Euler,γνωστή και ως εξίσωση Euler είναι η ισότητα: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+1=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Άλλες ισοδύναμες ταυτότητες του Euler είναι οι ισότητες: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-1=0 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) e=i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-2i/π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4) i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-π/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6) i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> =</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=cosπ+i·sinπ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=(-1)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">i</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">9) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-2i</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">4iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">6iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">8iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=√5 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">2.11 Ακριβείς σχέσεις μεταξύ π,φ,e και i </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;">Οι 16 ακριβείς σχέσεις που συνδέουν την χρυσή τομή φ,την σταθερά π,την σταθερά e και την φανταστική μονάδα i είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+φ=φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iφ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">i(φ+2π)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iφ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iφ+2iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iφ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=cos(φ+2∙π)+i∙sin(φ+2∙π) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) φ=e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6) φ=i∙[(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ/10</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(1-e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)] </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ/10</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-iπ/10</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=i/φ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8) 2∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=φ+i∙(3-φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">9) 2∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=φ+i∙(√5/φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) φ=2∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-2∙i∙sin(π/5) </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">11) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ/10</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=(i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2∙φ)+(1-1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4∙φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">12) φ=(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">4iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">6iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">8iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+1)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">13) φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">14) φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+2+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-2iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">15) φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=-(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">4iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-24iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">16) φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-iπ/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)+1 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p class="Paragraph SCXW240281116 BCX0" paraeid="{321b5d00-2bdb-49be-813f-99f04d2d0ddb}{8}" paraid="23183503" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-6330e405-7fff-87fe-44e5-4b245b051cfa"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;">Οι σχέσεις αυτές είναι οι πιο σημαντικές στα μαθηματικά γιατί συνδέουν τις τέσσερις βασικές μαθηματικές σταθερές. </span></p></div><div class="OutlineElement Ltr BCX0 SCXW240281116" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW240281116 BCX0" paraeid="{52b969cb-30ce-43d3-9902-509a51b7d5ab}{140}" paraid="972135031" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW240281116 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW240281116 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW240281116 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW240281116" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW240281116 BCX0" paraeid="{52b969cb-30ce-43d3-9902-509a51b7d5ab}{144}" paraid="651843475" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW240281116 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2.12 Ακριβής Μαγική σχέση που συνδέει έξι βασικές μαθηματικές σταθερές 0,1,π,φ,e και i</span></span></p><p class="Paragraph SCXW240281116 BCX0" paraeid="{52b969cb-30ce-43d3-9902-509a51b7d5ab}{144}" paraid="651843475" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span color="windowtext" style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;"><br /></span></p><p class="Paragraph SCXW240281116 BCX0" paraeid="{52b969cb-30ce-43d3-9902-509a51b7d5ab}{144}" paraid="651843475" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span color="windowtext" style="background-color: transparent; font-size: 12pt;"></span><span color="windowtext" style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;"> Η παρακάτω σχέση συνδέει έξι βασικές μαθηματικές σταθερές,τον αριθμό 0,τον αριθμό 1,τον αριθμό π,τον αριθμό φ,τον αριθμό e και τον φανταστικό αριθμό i: </span></p></div><div class="OutlineElement Ltr BCX0 SCXW240281116" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p class="Paragraph SCXW240281116 BCX0" paraeid="{52b969cb-30ce-43d3-9902-509a51b7d5ab}{154}" paraid="1571879945" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-ffe0f38c-7fff-ac1c-f15f-94dfc7e7ad99"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1+φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1+φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-iπ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">φ</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=0 </span></p></div><div class="OutlineElement Ltr BCX0 SCXW240281116" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW240281116 BCX0" paraeid="{52b969cb-30ce-43d3-9902-509a51b7d5ab}{176}" paraid="1608296040" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; font-size: 12px; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span class="EOP SCXW240281116 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-family: verdana; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"><br /></span></p><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{52b969cb-30ce-43d3-9902-509a51b7d5ab}{218}" paraid="1920297422" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; font-weight: bold; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3.Προσεγγιστικές σχέσεις μαθηματικών σταθερών</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{52b969cb-30ce-43d3-9902-509a51b7d5ab}{224}" paraid="1072436633" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{52b969cb-30ce-43d3-9902-509a51b7d5ab}{228}" paraid="1643277324" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3.1 Προσεγγιστικές σχέσεις μεταξύ φ και π</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{52b969cb-30ce-43d3-9902-509a51b7d5ab}{234}" paraid="1638912820" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Οι 25 προσεγγιστικές σχέσεις μεταξύ της χρυσής τομής φ και της σταθεράς π είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) π≃φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">(π+φ)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,14.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) φ≃2∙(log</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π)-π=1,61......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) π≃4</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">√φ=3,14..........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p class="Paragraph SCXW228396083 BCX0" paraeid="{52b969cb-30ce-43d3-9902-509a51b7d5ab}{238}" paraid="2022714008" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-57465941-7fff-2c97-1612-4ccb1e53cfca"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,01%. </span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{55}" paraid="1476037176" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{59}" paraid="2085434637" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">4) π≃6∙φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(2∙φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">5</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-1)=3,141.........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{75}" paraid="1166233955" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{79}" paraid="1168679885" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5) φ≃(π</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2π-6)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/5</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1,618...........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{93}" paraid="814923635" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{97}" paraid="403226416" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6) π≃3∙(φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+5)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">5=3,141</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">.........</span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{113}" paraid="786657705" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{117}" paraid="606216102" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">7) π≃6∙φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">5=3,141</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">.........</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;"> </span></span></span></p><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{117}" paraid="606216102" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><br /></span></span></p><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{117}" paraid="606216102" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">με ακρίβεια σφάλματος 0,0001%.</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{135}" paraid="1559201416" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{139}" paraid="2054409745" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">8) φ≃(5∙π</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1,6180........</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span></span></p><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{139}" paraid="2054409745" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><br /></span></span></p><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{139}" paraid="2054409745" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">με ακρίβεια σφάλματος 1,2</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #202122; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">×10</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: #202122; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">.</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{163}" paraid="388284612" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{167}" paraid="1841117473" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">9) (12/7)∙logπ-2∙logφ≃1=0,99997044</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">..........</span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{175}" paraid="389995952" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{179}" paraid="584953378" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">10) [2∙φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">]-[(√2-1)∙4</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">π]≃0=0,000470957</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">..........</span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{199}" paraid="831131869" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{203}" paraid="583245112" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-11c421da-7fff-56ac-93a7-e8534f3c5805"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">11) π≃(6/5)∙log2+(24/5)∙logφ=3,14159......... </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{211}" paraid="449006624" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{215}" paraid="1997948493" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">12) π≃(48∙φ-37)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">8∙φ=3,141592</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">.........</span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{227}" paraid="796467501" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{231}" paraid="255777378" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">13) φ≃37</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">(48-8∙π)=1,6180339</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">..........</span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{243}" paraid="198735967" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{247}" paraid="1568859681" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">14) π≃[(802∙φ-801)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(602∙φ-601)]</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=3,1415926</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">.........</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> </span></span></span></p><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{247}" paraid="1568859681" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"><br /></span></span></span></p><p class="Paragraph SCXW228396083 BCX0" paraeid="{f2d1586f-202b-462b-8c06-b340ebade961}{247}" paraid="1568859681" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">με ακρίβεια σφάλματος 0,0000001%.</span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{10}" paraid="310713160" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{14}" paraid="1733353646" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">15) π≃(2</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">7</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙5</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙4.463</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">9.181∙φ)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/6</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3,1415926.........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{36}" paraid="886573300" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{40}" paraid="1071509479" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">16) φ≃2</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">7</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙5</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙4.463</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">9.181∙π</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">6</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1,6180339..........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{62}" paraid="903487911" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{66}" paraid="847914164" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">17) π≃(9.764.064φ+4.867.832</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">944.055φ+566.433)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1/2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3,141592653.............</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{80}" paraid="1702073938" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{84}" paraid="942539549" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">18) φ≃4.867.832-566.433∙π</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">944.055∙π</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-9.764.064=</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,618033988...</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">.....</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{104}" paraid="979880256" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{108}" paraid="1964791189" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-cae4f4a9-7fff-9c43-72be-52764821e2dc"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">19) φ≃ln(3∙π∙22</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">35)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">ln[(111∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/8)+(2/21)]=1,61803398874........... </span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{138}" paraid="2010116644" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{142}" paraid="645932668" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">20) φ≃(355</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">113∙π)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4/565</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙9349</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2/35</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,61803398874...</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{164}" paraid="865242444" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{168}" paraid="736705193" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">21) π≃(35</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3∙22</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">3</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)·[360·φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-2·φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-3</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+(3</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">]</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">φ</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=3,141592653.............</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{202}" paraid="2144522730" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{206}" paraid="886359365" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">22) π≃(14.212.169</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">12</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">6</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)-φ=3,1415926535897..............</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{220}" paraid="980983919" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{224}" paraid="1481536151" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">23) φ≃(14.212.169</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">12</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">6</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">)-π=</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,6180339887498...</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{242}" paraid="11429058" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{f0fe166e-9c3e-486e-bfdf-b8cf9fb0f004}{246}" paraid="1462681112" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">24) φ≃151.837.964∙π</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">294.810.267=</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,6180339887498948482...</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{3aae215f-a27f-4c8e-afad-46ee6aa85a38}{5}" paraid="1386353756" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">`</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{3aae215f-a27f-4c8e-afad-46ee6aa85a38}{11}" paraid="1384218177" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">25) φ≃11∙(40∙π</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+23∙π-70)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(502∙π</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-659∙π-185)</span></span></p><p class="Paragraph SCXW228396083 BCX0" paraeid="{3aae215f-a27f-4c8e-afad-46ee6aa85a38}{11}" paraid="1384218177" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><br /></span></span></p><p class="Paragraph SCXW228396083 BCX0" paraeid="{3aae215f-a27f-4c8e-afad-46ee6aa85a38}{11}" paraid="1384218177" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ=</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,6180339887498948482...</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{3aae215f-a27f-4c8e-afad-46ee6aa85a38}{33}" paraid="1464067176" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{3aae215f-a27f-4c8e-afad-46ee6aa85a38}{37}" paraid="1056057444" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3.2 Προσεγγιστικές σχέσεις μεταξύ π και e</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{3aae215f-a27f-4c8e-afad-46ee6aa85a38}{43}" paraid="1819974451" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Οι 45 προσεγγιστικές σχέσεις μεταξύ της σταθεράς π και της σταθεράς e είναι: </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) π≃2∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">√3=3,1.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) π≃128</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">15∙e=3,1.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.84537; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) π≃7∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">cos(5/2)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,14.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4) π≃(163)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-6=3,14......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) </span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃(4∙e-1)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,14..........</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,01%. </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6) e≃9-2∙π=2,71.........</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,01% </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.84537; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7) π≃e+tan(2/5)=3,141......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8) π≃3</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">sin(3∙e)=3,141........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">9) π≃(2∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/7</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,141.........</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,001% </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) π≃[e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(π-e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,141.........</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,00006% </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">11) e≃(π+1)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2,718........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">12)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃10=9,999838798..........</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,002% </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">13) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-π≃20=19,999099979..........</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,005% </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">14) 3</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">(π+e)</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃5=4,999973083............</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,000538% </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">15) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-Π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃0=0,000017673.........</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,000005% </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">16) (π+e+163)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃13=12,994609439........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">17) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1-e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃23=23,00081238.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">18) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-2∙(4∙π-1)≃0=0,007951404......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">19) (163/e)+(e/163)+(π/163)-60=0,000299061......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">20) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">∙[3+(4+√5)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">])</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=23,140406827........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">21) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃2=2,000893…....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">22) π≃2∙7</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(5-e/5)=3,1415......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">23) π≃ln[(7-e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2]=3,14159......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">24) e≃(5</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">93</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">6</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2,71828............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">25) π≃[(2+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,14159.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">26) π≃(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/3)+(19/28)=3,14159.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">27) π≃(69</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">163)+e=3,14159.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">28) π≃(920</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">157)-e=3,14159........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">29) π≃ln[e∙ln(4.979)]=3,141592........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">30) π≃[lnln(97+7/5)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,141592......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">31) π≃e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">75.709</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 21pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">66.137</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,1415926.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">32) π≃2+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">709</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 18pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">/</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5.354</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,1415926........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">33) e≃42∙π∙[(π/2)-ln(3∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2)]=2,71828182..........</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,00000003% </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">34) e≃2.100∙(10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">629)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2,71828182.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; padding: 0pt 0pt 10pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">35) π≃10∙tanh(28∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">15)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-(Π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)≃0=0,0000000006005.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">36) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-ln3-(159/5)∙ln2≃0=0,00000000023.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">37) e≃(1,000924472)∙[2∙(4/π)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">(π/4)4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2,718281828............ </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">38) (3.730∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e)-(879∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 13pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-419</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">.736≃0=0,0000000001622........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">39) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-π/9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-4π/9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-9π/9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-16π/9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-25π/9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-36π/9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-49π/9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-64π/9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-1≃0=0,0000000000010504..... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">40) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-7∙π-1-(-e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+28∙e+189</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">634∙e)≃0,000000000000377311....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">41) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-7∙π-(365.455</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">317.913)≃0=0,00000000000002805671....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">42) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-{20+π+1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">[1.111+1/(11+1/√2)]}≃0=0,000000000000063.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">43) e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-[17+√3+(172))</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+ln(ln9)]≃0=0,000000000000025........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">44) e≃[π-(12</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">ln889)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-1/4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2,7182818284590...........</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: -6.93898pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: -6.93898pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 2×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-19</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">.</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">45) π≃(12</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">ln889)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-4</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,14159265358979............</span></p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.44; margin-bottom: 0pt; margin-right: 10pt; margin-top: 0pt; text-align: justify;"><span id="docs-internal-guid-2bd98036-7fff-761c-5ba8-916a261ce62c"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">με ακρίβεια σφάλματος 2×10</span><span style="background-color: transparent; font-family: Verdana; font-size: 16pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">-19</span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">. Αυτές οι σχετικά απλές σχέσεις παρατηρούμε ότι έχουν καταπληκτική ακρίβεια. </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{11}" paraid="407776307" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{15}" paraid="1286098153" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3.3 Προσεγγιστικές σχέσεις μεταξύ φ και e</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{21}" paraid="820445783" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{25}" paraid="1277658437" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Οι 11 προσεγγιστικές σχέσεις μεταξύ της χρυσής τομής φ και της σταθεράς e είναι: </span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{39}" paraid="107223554" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{43}" paraid="1786741713" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1) φ≃(5∙e+4)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">4∙e=1</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">,</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">61..........</span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{57}" paraid="132318947" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{61}" paraid="1200343844" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2) e≃4</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">(4∙φ-5)=2,71</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">...........</span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{73}" paraid="1124243295" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{77}" paraid="93004640" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3) e≃φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-5</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-10</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-13</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2,7182.........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{99}" paraid="1303968506" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{103}" paraid="636643077" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">4) e≃φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">4</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">(φ+1)</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙2</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">1</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="14" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">/</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">(φ+1)</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">=2,7182</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">.........</span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{127}" paraid="1623977332" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{131}" paraid="870576623" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5) φ≃(2</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">6/e</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-4)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">-1</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=1,6180.............</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{145}" paraid="1042227242" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{149}" paraid="1488863903" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6) e≃6⋅7⋅φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">5</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">=2,7182........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{163}" paraid="2116061300" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{167}" paraid="933705305" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">7) φ≃5</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">∙e</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">6⋅7=1,6</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">180.............</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{183}" paraid="1575306461" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{187}" paraid="1106504658" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">8) 1</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">e+1</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ+1</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">71</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃1=0,999997937...........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{207}" paraid="1771810497" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{211}" paraid="1110511666" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">9) </span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">√</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">e+1</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">φ</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">+1</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">87</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃1=0,999990924............</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{239}" paraid="471039161" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{243}" paraid="761680584" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">10) φ≃[√63∙(3-e)+1]</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 14pt; font-variant-ligatures: none; line-height: 24.8208px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">2=1,61803.........</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{df188868-4772-4fc4-9c8d-e94887199e25}{253}" paraid="757607654" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{531bbcc6-cd2c-4388-9003-14ec317f7e31}{2}" paraid="1330990471" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">11) φ≃(711∙e</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-906∙e-487)</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 16pt; font-variant-ligatures: none; line-height: 26.9792px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">/</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">(175∙e</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">2</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">-56∙e+283)=</span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">1,6180339887498948482...</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">....</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{531bbcc6-cd2c-4388-9003-14ec317f7e31}{24}" paraid="1464680140" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{531bbcc6-cd2c-4388-9003-14ec317f7e31}{28}" paraid="180578959" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">3.4 Προσεγγιστικές σχέσεις μεταξύ π και i</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{531bbcc6-cd2c-4388-9003-14ec317f7e31}{34}" paraid="1996894155" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{531bbcc6-cd2c-4388-9003-14ec317f7e31}{38}" paraid="1185041427" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"> </span></span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Η 1 προσεγγιστική σχέση μεταξύ της σταθεράς π και της φανταστικής μονάδας i είναι: </span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{531bbcc6-cd2c-4388-9003-14ec317f7e31}{50}" paraid="2054663338" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{531bbcc6-cd2c-4388-9003-14ec317f7e31}{54}" paraid="1486740268" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">1) (π+20</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">)</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 9.5pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun Superscript SCXW228396083 BCX0" data-fontsize="12" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text; vertical-align: super;">i</span></span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR">≃-1</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{531bbcc6-cd2c-4388-9003-14ec317f7e31}{66}" paraid="724417005" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{531bbcc6-cd2c-4388-9003-14ec317f7e31}{70}" paraid="1148746283" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;">3.5 Προσεγγιστικές σχέσεις μεταξύ </span><span class="SpellingError SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-image: url("data:image/gif;base64,R0lGODlhBQAEAJECAP////8AAAAAAAAAACH5BAEAAAIALAAAAAAFAAQAAAIIlGAXCCHrTCgAOw=="); background-position: 0% 100%; background-repeat: repeat-x; border-bottom: 1px solid transparent; margin: 0px; padding: 0px; user-select: text;">φ,π</span><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"> και e</span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{531bbcc6-cd2c-4388-9003-14ec317f7e31}{76}" paraid="1395671809" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;">Οι 28 προσεγγιστικές σχέσεις μεταξύ της σταθεράς π,της χρυσής τομής φ και της σταθεράς e είναι:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) e≃(φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 10.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">π/e</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2,71........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,07% </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2) φ≃357∙π-412∙e=1,61......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3) e≃3∙φ-π+1=2,71......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">4) (φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-(3/2)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">12</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">7</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃0=0,000286948.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5) φ≃e-(π)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/12</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=1,618.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6) e≃π+φ+(1-π∙φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">2=2,718........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7) π≃[(6∙e∙φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,141.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">8) π≃[φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-(1</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=3,141....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,02% </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">9) π≃5∙φ∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">7=3,141....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 1,5×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10) e≃π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">12/7</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2,7182........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">11) e≃[(2∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+2∙π-φ-1)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3]-π∙φ=2,7182.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">12) e≃7∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6∙φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=2,7182........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">13) φ≃[7∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">6∙e]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=1,6180........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">14) φ≃7∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙e=1,6180....... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 1,5×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">15) e≃7∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5∙φ=2,7182........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 1,5×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">16) e≃(6∙φ-2∙π+2∙π∙φ)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5=2,71828........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">17) φ≃[5∙(1+π)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e]-6=1,6180339........ </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 1×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-6</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">18) π≃[</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">∙(φ+6)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">5]-1=3,1415926......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">19) φ≃14∙(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">19</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">22</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=1,6180339......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">20) π≃(2∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(e-1)-[(2∙φ-1)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(100-36/10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">−5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)]=3,1415926535.........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 1×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">21) φ≃14∙(e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">19</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">22</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/5</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">∙(10∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">8</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">9</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/531</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">=1,6180339887.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">22) (φ+e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">314.393.388.446.503</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">402.909.889.100.000</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃1,0000000000000018.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">23) (φ+e))</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">314.393.388.446.503</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">402.909.889.100.000</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃π=3,14159265358979......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">24) φ≃(1.967.981∙π-314.270∙e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">3.293.083=1,618033988749894...........</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"> </p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 2×10</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">-16</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">25) e≃1.400∙φ-2.410∙π+1.082</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">906∙φ-1.016∙π+172=2,71828182845904523.......... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">26) φ≃-π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+2∙π-3∙e-13+√2-log2-log3</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-3∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">3</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-π-e+7∙√2+7∙√3-3∙log2 </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Με αριθμητική τιμή για την χρυσή αναλογία φ=1,618033988749894848........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">27) φ≃(1/42)∙[22∙π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-56∙e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+50∙π-34∙e-5∙(1+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+7∙(1+e)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+20∙(1+π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-24∙(1+π)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">1/2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-1] </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> Με αριθμητική τιμή για την χρυσή αναλογία φ=1,6180339887498948482........... </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">28) e≃(45.483∙φ-2.961∙π-18.765)</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">16.748</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;"> Αυτή η προσεγγιστική σχέση έχει την μεγαλύτερη ακρίβεια με αριθμητική τιμή για την σταθερά e=2,718281828459045235360........</span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{95d6a8ad-1862-4022-95d7-d08d76de27ef}{255}" paraid="1418736253" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EL-GR" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EL-GR"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">3.6 Προσεγγιστική σχέση μεταξύ i,π και e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; text-align: left; white-space: pre-wrap;"> Η 1 προσεγγιστική σχέση που συνδέει την χρυσή τομή φ,την σταθερά π,την σταθερά e και την φανταστική μονάδα i είναι:</span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">1) π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">ie</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">-1≃2=1,99977658867............. </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre;">3.7 Προσεγγιστική σχέση μεταξύ φ,i,π και e </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre;"><span style="background-color: transparent; font-size: 12pt; text-align: left; white-space: pre-wrap;"> Η 1 προσεγγιστική σχέση που συνδέει την χρυσή τομή φ,την σταθερά π,την σταθερά e και την φανταστική μονάδα i είναι: </span> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">φ</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+e</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">+(i</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">/</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">e)]</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">≃π</span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 9.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"> </span></p><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{4}" paraid="1955256471" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span id="docs-internal-guid-9378e3b2-7fff-20b5-c940-6243584ed870"></span></p><p dir="ltr" style="background-color: white; line-height: 1.2; margin-bottom: 0pt; margin-right: 9.56102pt; margin-top: 0pt; text-align: justify;"><span style="background-color: transparent; color: black; font-family: Verdana; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">με ακρίβεια σφάλματος 0,02% </span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{116}" paraid="602487651" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{120}" paraid="1639596392" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; font-weight: bold; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">ΒΙΒΛΙΟΓΡΑΦΙΑ</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{126}" paraid="1893236972" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN"><span class="NormalTextRun SCXW228396083 BCX0" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; user-select: text;"></span></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{130}" paraid="696897224" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[1] </span><a class="Hyperlink SCXW228396083 BCX0" href="https://www.en.wikipedia.org/" rel="noreferrer noopener" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; text-decoration-line: none; user-select: text;" target="_blank"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: black; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">www.en.wikipedia.org/</span></a><span class="TextRun EmptyTextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN"></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{139}" paraid="1985085379" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[2] </span><a class="Hyperlink SCXW228396083 BCX0" href="http://www.wolframalpha.com/" rel="noreferrer noopener" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; text-decoration-line: none; user-select: text;" target="_blank"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: black; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">www.wolframalpha.com/</span></a><span class="TextRun EmptyTextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN"></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{148}" paraid="363141011" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[3] www.</span><a class="Hyperlink SCXW228396083 BCX0" href="https://math.stackexchange.com/" rel="noreferrer noopener" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; margin: 0px; padding: 0px; text-decoration-line: none; user-select: text;" target="_blank"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; color: black; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">math.stackexchange.com/</span></a><span class="TextRun EmptyTextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN"></span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{157}" paraid="1352686058" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[4] www.mathworld.wolfram.com/ </span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{163}" paraid="645952511" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[5] www.numberempire.com/</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{169}" paraid="1519142714" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[6] http://www.contestcen.com/pi.htm</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{175}" paraid="1623266529" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[7] https://archive.lib.msu.edu/crcmath/math/math/p/p303.htm </span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{181}" paraid="1576697599" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[8] https://archive.lib.msu.edu/crcmath/math/math/e/e001.htm</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{187}" paraid="926740902" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[9] https://www.primepuzzles.net/puzzles/puzz_050.htm</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{193}" paraid="1178410089" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[10] Panagiotis Stefanides</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN"> </span><span class="TextRun SCXW228396083 BCX0" data-contrast="auto" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">http://www.stefanides.gr/Html/pi.html</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{203}" paraid="17289283" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[11] Frank Michael Jackson Extending Euler's identity to include Phi, the golden ratio</span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; font-variant-ligatures: none; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN"> </span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 11pt; line-height: 19.425px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{211}" paraid="1380585180" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">www.researchgate.net/publication/292983417_Extending_Euler's_identity_to_include_Phi_the_golden_ratio</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{217}" paraid="469772953" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[12] Binh Ho On the Approximate Relationship between Pi, Euler’s Number, and the Golden Ratio Constant </span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{223}" paraid="1858630813" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 10.5pt; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 18.3458px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">DOI: </span><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">10.13140/RG.2.2.17490.91843</span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{231}" paraid="58073886" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">[13] William H. Press Seemingly Remarkable Mathematical Coincidences Are Easy to Generate </span><span class="EOP SCXW228396083 BCX0" data-ccp-props="{"201341983":0,"335551550":6,"335551620":6,"335559739":160,"335559740":259}" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;"> </span></span></p></div><div class="OutlineElement Ltr BCX0 SCXW228396083" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; clear: both; cursor: text; direction: ltr; font-size: 12px; margin: 0px; overflow: visible; padding: 0px; position: relative; user-select: text;"><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{237}" paraid="775593738" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="font-family: verdana;"><span class="TextRun SCXW228396083 BCX0" data-contrast="none" face="Verdana, Verdana_EmbeddedFont, Verdana_MSFontService, sans-serif" lang="EN" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; font-size: 12pt; font-variant-ligatures: none; line-height: 20.5042px; margin: 0px; padding: 0px; user-select: text;" xml:lang="EN">https://web.archive.org/web/20120312092311/http://www.nr.com/whp/NumericalCoincidences.pdf</span></span></p><p class="Paragraph SCXW228396083 BCX0" paraeid="{bada702a-7e45-4b02-b6f1-7c68eea3ae7b}{237}" paraid="775593738" style="-webkit-tap-highlight-color: transparent; -webkit-user-drag: none; background-color: transparent; color: windowtext; font-kerning: none; margin: 0px; overflow-wrap: break-word; padding: 0px; text-align: justify; user-select: text; vertical-align: baseline;"><span style="background-color: transparent; font-family: Verdana; font-size: 12pt; white-space: pre-wrap;">[14] Michele Nardelli,Antonio Nardelli On the Ramanujan’s Fundamental Formula for obtain a highly precise Golden Ratio: mathematical connections with Black Holes Entropies and Like-Particle Solutions https://vixra.org/pdf/1909.0456v1.pdf </span></p></div></div></div></div></div>ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.com0tag:blogger.com,1999:blog-6644102595821010388.post-75605964092705805252020-12-01T11:53:00.005-08:002020-12-06T09:47:00.205-08:00ΑΡΝΗΤΙΚΗ ΜΑΖΑ<p> <b><span style="color: red; font-family: verdana; font-size: x-large;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ</span></b></p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoRt42vLFO57oeIUXtiQUHnQE5Ef26OxlZRCaJrKH7l8U-MN_oIHWDLaQFOCsO09VmL8kOI36pW9K9kA1QqDOw4npu6KZPkEbhwgeZGlpjUyA4IR6OM8I5-Fc_cd7nzLMWtJyHOUBB3dc/s1920/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259121.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1080" data-original-width="1920" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoRt42vLFO57oeIUXtiQUHnQE5Ef26OxlZRCaJrKH7l8U-MN_oIHWDLaQFOCsO09VmL8kOI36pW9K9kA1QqDOw4npu6KZPkEbhwgeZGlpjUyA4IR6OM8I5-Fc_cd7nzLMWtJyHOUBB3dc/w640-h360/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259121.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b style="text-align: left;"><span style="color: #800180; font-family: verdana; font-size: large;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ</span></b></td></tr></tbody></table><p></p><p></p><p><b style="color: red; text-align: justify;"><span style="font-family: verdana;">ΕΙΣΑΓΩΓΗ</span></b></p><p style="text-align: justify;"><span style="font-family: verdana;"> <b><span style="color: #2b00fe;">Αρνητική μάζα</span>,στη θεωρητική φυσική,ονομάζεται ένας τύπος εξωτικής ύλης του οποίου η μάζα έχει αντίθετο πρόσημο από την κανονική ύλη.</b>Για παράδειγμα η αρνητική μάζα μπορεί να πάρει την τιμή<b> −1 kg.</b>Η αρνητική μάζα είναι μια υποθετική μορφή ύλης της οποίας η ύπαρξη δεν έχει αποδειχτεί,παρόλο που δεν αντιτίθεται σε κάποιον νόμο της <b>Φυσικής</b>.</span><span style="font-family: verdana; text-align: left;">Υποθετικά,η ύλη μπορεί να έχει αρνητική μάζα με την ίδια έννοια που ένα ηλεκτρικό φορτίο μπορεί να είναι είτε αρνητικό είτε θετικό.</span><span style="font-family: verdana; text-align: left;">Οι άνθρωποι σπάνια σκέφτονται με αυτούς τους όρους,και ο καθημερινός μας κόσμος βλέπει μόνο τις θετικές πτυχές του δεύτερου νόμου κίνησης του <b>Isaac Newton</b>.</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhC6LAmuGK5_rAuNHEe5OdZXNx9GD1xlGkKKHMJMKsKOW14pahqplipMXGWAmgymUx21gGdUTURTX1mRG07efc7kmQVpQscq1XlQKh0-SljLj36mx2IGlOzen0wiGK7OIM-aE9V30L2Qkg/s504/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259113.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="322" data-original-width="504" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhC6LAmuGK5_rAuNHEe5OdZXNx9GD1xlGkKKHMJMKsKOW14pahqplipMXGWAmgymUx21gGdUTURTX1mRG07efc7kmQVpQscq1XlQKh0-SljLj36mx2IGlOzen0wiGK7OIM-aE9V30L2Qkg/s16000/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259113.jpg" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b style="text-align: justify;"><span style="color: #800180; font-family: verdana;"><span>Αρνητική μάζα</span>,στη θεωρητική φυσική,ονομάζεται ένας τύπος εξωτικής ύλης του οποίου η μάζα έχει αντίθετο πρόσημο από την κανονική ύλη</span></b></td></tr></tbody></table><span style="font-family: verdana;"><span style="font-family: verdana;"></span></span><p></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: left;"><span style="background-color: white;"> </span>Τέτοια ύλη θα παραβίαζε μία ή περισσότερες ενεργειακές συνθήκες και θα έδειχνε κάποιες παράξενες ιδιότητες,που απορρέουν από την ασάφεια ως προς το εάν η έλξη πρέπει να αναφέρεται στη δύναμη ή στην αντίθετα προσανατολισμένη επιτάχυνση της αρνητικής μάζας.Χρησιμοποιείται σε ορισμένες κερδοσκοπικές υποθετικές τεχνολογίες,όπως ο </span><b style="font-family: verdana; text-align: left;">χρόνος ταξιδιού στο παρελθόν</b><span style="font-family: verdana; text-align: left;">,η </span><b style="font-family: verdana; text-align: left;">κατασκευή ανιχνεύσιμων σκουληκότρυπων</b><span style="font-family: verdana; text-align: left;">,η μονάδα </span><b style="font-family: verdana; text-align: left;">δίσκου Alcubierre</b><span style="font-family: verdana; text-align: left;"> και πιθανώς άλλων </span><b style="font-family: verdana; text-align: left;">τύπων μονάδων στημόνων</b><span style="font-family: verdana; text-align: left;">.Επί του παρόντος,ο πλησιέστερος γνωστός πραγματικός εκπρόσωπος τέτοιας εξωτικής ύλης είναι μια περιοχή πυκνότητας αρνητικής πίεσης που παράγεται από το </span><b style="font-family: verdana; text-align: left;">φαινόμενο Casimir</b><span style="font-family: verdana; text-align: left;">.</span></p><p></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz0WWOoWDnkbBONgjyW-oD0d4y9TRhg2PlNeBWfrOGcxW_gmeaTLQnpJLgdS344BzMiFb2SwkucQrVRkzRPtJhvKuGNnh90FlR7P1hgq-FDB5W0R7WptRwyMOQD47TUlAzYCIb0pUo9Ok/s696/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259122.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="363" data-original-width="696" height="334" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz0WWOoWDnkbBONgjyW-oD0d4y9TRhg2PlNeBWfrOGcxW_gmeaTLQnpJLgdS344BzMiFb2SwkucQrVRkzRPtJhvKuGNnh90FlR7P1hgq-FDB5W0R7WptRwyMOQD47TUlAzYCIb0pUo9Ok/w640-h334/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259122.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white; box-sizing: border-box; color: #800180; font-family: verdana; text-align: left; vertical-align: inherit;"><b>Υποθετικά,η ύλη μπορεί να έχει αρνητική μάζα με την ίδια έννοια που ένα ηλεκτρικό φορτίο μπορεί να είναι είτε αρνητικό είτε θετικό</b></span></td></tr></tbody></table><span style="background-color: white; color: #202122; font-family: verdana;"><div style="text-align: justify;"><span style="color: #202122; font-family: verdana;"> </span><span style="font-family: verdana;">Η αρνητική μάζα είναι οποιαδήποτε περιοχή του χώρου στην οποία για ορισμένους παρατηρητές η πυκνότητα μάζας μετριέται ως αρνητική.Αυτό θα μπορούσε να συμβεί λόγω μιας περιοχής του χώρου στην οποία η συνιστώσα τάσης του <b>τανυστή τάσης-ενέργειας Einstein</b> είναι μεγαλύτερη σε μέγεθος από την πυκνότητα μάζας.</span><span style="font-family: verdana;">Όλα αυτά είναι παραβιάσεις μιας ή άλλης παραλλαγής της θετικής ενεργειακής κατάστασης της γενικής θεωρίας της σχετικότητας του </span><b style="background-color: transparent;">Αϊνστάιν</b><span style="font-family: verdana;">.Ωστόσο,η θετική ενεργειακή κατάσταση δεν είναι απαραίτητη προϋπόθεση για τη μαθηματική συνέπεια της θεωρίας.</span></div></span><p></p><p></p><p style="text-align: justify;"><span style="color: red; font-family: verdana;"><b>ΙΣΤΟΡΙΑ ΤΗΝ ΑΡΝΗΤΙΚΗΣ ΜΑΖΑΣ</b></span></p><p style="text-align: justify;"><span style="font-family: verdana;"><span style="color: red;"><b> </b></span>Η έννοια της αρνητικής μάζας είναι καθαρά θεωρητική.Οι </span><span style="text-align: left;"><span style="font-family: verdana;">σημειώσεις του <b>Άλμπερτ Αϊνστάιν </b>από το <b>1918</b> δείχνουν ότι από τότε εξέταζε την πιθανότητα ύπαρξης αρνητικών μαζών στο σύμπαν.</span></span><span style="font-family: verdana;">Ο <b>Joaquin Mazdak Luttinger</b> ήταν από τους πρώτους που εξέτασε την συμπεριφορά της υποθετικής αρνητικής μάζας κάτω από βαρυτικές και άλλες δυνάμεις.Αυτό έγινε διαμέσου μιας εργασίας σ</span><span style="background-color: white; color: #202122; font-family: verdana;">το δοκίμιο του </span><b style="background-color: white; color: #202122; font-family: verdana;">4ου βραβείου </b><span style="font-family: verdana;">που υπέβαλλε το</span><b style="font-family: verdana;"> 1951</b><span style="font-family: verdana;"> </span><span style="background-color: white; color: #202122; font-family: verdana;">για τον διαγωνισμό του</span><span style="font-family: verdana;"> </span><b style="font-family: verdana;">Gravity Research Foundation </b><span style="font-family: verdana;">με τίτλο </span><b style="font-family: verdana;">«On ‘negative’ mass in the theory of gravitation»</b><span style="font-family: verdana;">.</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijh8-pvozUHa2gJET6jUrG6TeNEvTrCuLiGNFpIQcw3935LMTFctgyBXJMaa99bOdCoMjU3GCqxlr1A0VblHdey5V_wY_-InZqQWPem-WohNFE9YEaMdmh1gLMyhurbDy-knIkeSEuDf0/s650/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259122.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="375" data-original-width="650" height="370" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijh8-pvozUHa2gJET6jUrG6TeNEvTrCuLiGNFpIQcw3935LMTFctgyBXJMaa99bOdCoMjU3GCqxlr1A0VblHdey5V_wY_-InZqQWPem-WohNFE9YEaMdmh1gLMyhurbDy-knIkeSEuDf0/w640-h370/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259122.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="color: #800180;"><b><span style="font-family: verdana; text-align: justify;">Η υπόθεση ύπαρξης και αρνητικών μαζών </span><span style="font-family: verdana; text-align: justify;">με την βοήθεια της </span><span style="font-family: verdana; text-align: justify;">Γενικής Θεωρίας της Σχετικότητας</span><span style="font-family: verdana; text-align: justify;"> του </span><span style="font-family: verdana; text-align: justify;">Άλμπερτ Αϊνστάιν</span></b></span></td></tr></tbody></table><p></p><p style="text-align: justify;"><span style="font-family: verdana;"> Το <b>1957</b> ακολουθώντας την ιδέα του <b>Luttinger</b>,ο <b>Hermann Bondi</b> εξέτασε κι αυτός </span><span style="color: #202122; font-family: verdana;">σε μια δημοσίευση στο περιοδικό</span><span face="sans-serif" style="color: #202122; font-size: 14px; text-align: start;"> </span><i style="color: #202122; text-align: start;"><span style="font-family: verdana;"><b>Reviews</b></span></i><span style="color: #202122; font-family: verdana;"><b> of Modern Physics</b></span><span style="font-family: verdana;"> </span><span style="font-family: verdana;">την υπόθεση ύπαρξης και αρνητικών μαζών </span><span style="font-family: verdana;">με την βοήθεια της </span><b style="font-family: verdana;">Γενικής Θεωρίας της Σχετικότητας</b><span style="font-family: verdana;"> του </span><b style="font-family: verdana;">Άλμπερτ Αϊνστάιν</b><span style="font-family: verdana;"><b>.</b>Κατέληξε στο συμπέρασμα ότι δεν υπάρχει κάποια λογική αντίφαση στο να υπάρχουν και αρνητικές μάζες,αρκεί και τα τρία είδη των μαζών,η αδρανειακή,η βαρυτική παθητική και η βαρυτική ενεργητική μάζα να είναι αρνητικές,</span><span style="background-color: white; color: #202122; font-family: verdana;">αλλά ότι η υπόθεση της αρνητικής μάζας περιλαμβάνει κάποια αντι-διαισθητική μορφή κίνησης.Για παράδειγμα,ένα αντικείμενο με αρνητική αδρανειακή μάζα αναμένεται να επιταχυνθεί προς την αντίθετη κατεύθυνση με εκείνη στην οποία ωθήθηκε (μη βαρυτικά).</span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiLgC4hsYkwXtxeGfOSseI2gJ-iALLRpBlTw7dCqTlN40qPxryGMeQ7D230ngUVKwxLEzOQQD9jmBeglcqvn6Uy_WGwSKr0JcTDouGXxHHDOTKMKWS21cC446SvdXyu5JyKDuunHBv848/s400/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%2591.jpg" style="margin-left: auto; margin-right: auto;"><span style="font-family: verdana;"><img border="0" data-original-height="389" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiLgC4hsYkwXtxeGfOSseI2gJ-iALLRpBlTw7dCqTlN40qPxryGMeQ7D230ngUVKwxLEzOQQD9jmBeglcqvn6Uy_WGwSKr0JcTDouGXxHHDOTKMKWS21cC446SvdXyu5JyKDuunHBv848/s320/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%2591.jpg" width="320" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="color: #800180; font-family: verdana;"><b>Ο Sir Hermann Bondi KCB FRS (1 Νοεμβρίου 1919-10 Σεπτεμβρίου 2005) ήταν Αυστριακοβρετανός μαθηματικός και κοσμολόγος.Είναι γνωστός για την ανάπτυξη του μοντέλου σταθερής κατάστασης του σύμπαντος με τους Fred Hoyle και Thomas Gold ως εναλλακτική λύση στη θεωρία του Big Bang.Συνέβαλε στη θεωρία της γενικής σχετικότητας,και ήταν ο πρώτος που ανέλυσε την αδρανειακή και βαρυτική αλληλεπίδραση της αρνητικής μάζας και ο πρώτος που εξήγησε σωστά τη φύση των βαρυτικών κυμάτων.Στην αυτοβιογραφία του 1990,ο Bondi θεώρησε το έργο του 1962 για τα βαρυτικά κύματα ως το "καλύτερο επιστημονικό έργο" του </b></span></td></tr></tbody></table><span style="color: #202122; font-family: verdana;"><div style="text-align: justify;"> Υπήρξαν πολλές άλλες αναλύσεις αρνητικής μάζας, όπως οι μελέτες που διεξήχθησαν από την <b>RM Price</b>,ωστόσο καμία δεν έθιξε το ζήτημα του τι είδους ενέργεια και ορμή θα ήταν απαραίτητη για την περιγραφή της μη μοναδικής αρνητικής μάζας.Πράγματι,η λύση <b>Schwarzschild</b> για την παράμετρο αρνητικής μάζας έχει μια γυμνή μοναδικότητα σε μια σταθερή χωρική θέση.</div><div style="text-align: justify;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_rtzwnygVDKdjZ3UIBEv2ushABzVkR8irqHZlmntDvvXsdFy3fI3CAY4CFxc0BA1OAO7dLFDzMMjedmkSeWaejkhNYAv_9t1eGuvEXhQXKkoBeARPA6JjstQS1Bh3PKBbbrZm2YEV0R8/s980/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259119.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="425" data-original-width="980" height="278" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_rtzwnygVDKdjZ3UIBEv2ushABzVkR8irqHZlmntDvvXsdFy3fI3CAY4CFxc0BA1OAO7dLFDzMMjedmkSeWaejkhNYAv_9t1eGuvEXhQXKkoBeARPA6JjstQS1Bh3PKBbbrZm2YEV0R8/w640-h278/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259119.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><span style="color: #800180; font-family: verdana;">Η θετική μάζα με μπλε χρώμα στην εικόνα προκαλεί ένα βαρυτικό δυναμικό το σχήμα ενός φρεατίου βαρύτητας όπου εμπίπτουν και άλλες μάζες.Αυτός είναι ο λόγος που η ύλη είναι πάντα ελκτική.Κλασικά στη γενική σχετικότητα,η υποθετική «εξωτική ύλη» από αρνητική μάζα με κόκκινο χρώμα στην εικόνα θα προκαλούσε αντίθετα ένα αντίθετο βαρυτικό δυναμικό στο χωροχρόνο,το σχήμα ενός λόφου βαρύτητας.Ένα τέτοιο αρνητικό βαρυτικό δυναμικό θα αποκρούσει οποιαδήποτε άλλη μάζα γύρω,συμπεριλαμβανομένων άλλων αρνητικών μαζών</span></b></td></tr></tbody></table> Το ερώτημα που τίθεται αμέσως είναι,δεν θα ήταν δυνατόν να εξομαλυνθεί η μοναδικότητα με κάποιο είδος αρνητικής πυκνότητας μάζας.Η απάντηση είναι ναι,αλλά όχι με ενέργεια και ορμή που ικανοποιεί την κυρίαρχη ενεργειακή κατάσταση.Αυτό οφείλεται στο γεγονός ότι,αν ικανοποιεί την ενέργεια και την ορμή η κυρίαρχη κατάσταση της ενέργειας μέσα σε ένα χωροχρόνο που είναι ασυμπτωτικά επίπεδη,η οποία θα ήταν η περίπτωση της εξομάλυνσης της λύσης μάζας <b>Schwarzschild </b>μοναδική αρνητική,τότε θα πρέπει να ικανοποιεί τη θετική ενέργεια,δηλαδή της μάζας <b>ADM</b> πρέπει να να είστε θετικοί,κάτι που φυσικά δεν ισχύει.Ωστόσο,παρατηρήθηκε από τους <b>Belletête</b> και <b>Paranjape</b> ότι,δεδομένου ότι το θεώρημα θετικής ενέργειας δεν ισχύει για το ασυμπτωτικό <b>διάστημα Sitter</b>,θα ήταν πραγματικά δυνατό να εξομαλυνθεί,με ενέργεια-ορμή που ικανοποιεί την κυρίαρχη ενεργειακή κατάσταση,την μοναδικότητα της αντίστοιχης ακριβής λύση αρνητικής μάζας <b>Schwarzschild–de Sitter</b>,που είναι η μοναδική ακριβής λύση των εξισώσεων του Αϊνστάιν με την κοσμολογική σταθερά.</div><div style="text-align: justify;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnfMNSjxj-IzX8Sg5ceRzZ4FunWK4AddrWokbuMMV23pkNe0fg4kE4fXZLdlgi5SnAY7y6W6qCY0PqdoA1yCF7f66iSV02F8mligppvIbIHCpvDUW6lDveOAgPXPDBNoS3dtCdTpsjIIw/s980/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259120.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="425" data-original-width="980" height="278" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnfMNSjxj-IzX8Sg5ceRzZ4FunWK4AddrWokbuMMV23pkNe0fg4kE4fXZLdlgi5SnAY7y6W6qCY0PqdoA1yCF7f66iSV02F8mligppvIbIHCpvDUW6lDveOAgPXPDBNoS3dtCdTpsjIIw/w640-h278/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259120.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="color: #800180; font-family: verdana;"><b>Το μοντέλο Janus</b></span></td></tr></tbody></table> Σε ένα επόμενο άρθρο,οι <b>Mbarek </b>και <b>Paranjape</b> έδειξαν ότι στην πραγματικότητα είναι δυνατόν να επιτευχθεί η απαιτούμενη παραμόρφωση μέσω της εισαγωγής της δυναμικής ενέργειας-ορμής ενός τέλειου υγρού.<span style="font-family: verdana; text-align: left;">Ο </span><b style="text-align: left;">Bondi</b><span style="font-family: verdana; text-align: left;">,όπως και όσοι ασχολήθηκαν με το ζήτημα,διαπίστωσαν ότι η εμπλοκή σωμάτων με αρνητική μάζα δημιουργεί κάποια απροσδόκητα και διασκεδαστικά φαινόμενα κόντρα στην διαίσθησή μας.</span></div></span><div><p></p><p style="text-align: justify;"><span style="color: red; font-family: verdana;"><b>ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΣΤΟ ΕΡΓΑΣΤΗΡΙΟ</b></span></p><p style="text-align: justify;"><span style="text-align: left;"><span style="font-family: verdana;"> Το <b>2017 </b></span></span><span style="font-family: verdana;">φυσικοί του <b>Πανεπιστημίου </b>της <b>Ουάσιγκτον</b> </span><span style="font-family: verdana; text-align: left;"><b>Washington State University</b> </span><span style="font-family: verdana;">ανακοίνωσαν πως δημιούργησαν στο εργαστήριο </span><span style="font-family: verdana; text-align: left;">ένα υγρό με </span><span style="font-family: verdana;">αρνητική μάζα.Έτσι</span><b style="font-family: verdana; text-align: left;"> </b><span style="font-family: verdana; text-align: left;">έγινε η πρώτη δημιουργία αρνητικής μάζας μέσα σε επιστημονικά εργαστήρια.</span><span style="font-family: verdana;">Προφανώς δεν ανίχνευσαν,ούτε δημιούργησαν σωματίδια με αρνητική μάζα,έκαναν όμως το υπερρευστό ρουβίδιο να συμπεριφέρεται σαν να είχε αρνητική μάζα.</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggZDWZz0k2fvSqB5g0orPV1V3KGXdESVN2Ya7hMB4u2P0noxm_RJapV5-DFuUqIYoV8MUgBV0SlDK9WNOLetpaEw8V1G15pe7UJHk3L3WNo72DeeOHiL2YWZ4feWzKjay56da5CHr3JDI/s770/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%25912.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="433" data-original-width="770" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggZDWZz0k2fvSqB5g0orPV1V3KGXdESVN2Ya7hMB4u2P0noxm_RJapV5-DFuUqIYoV8MUgBV0SlDK9WNOLetpaEw8V1G15pe7UJHk3L3WNo72DeeOHiL2YWZ4feWzKjay56da5CHr3JDI/w640-h360/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%25912.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="color: #800180;"><b><span style="text-align: left;"><span style="font-family: verdana;">Το 2017 </span></span><span style="font-family: verdana; text-align: justify;">φυσικοί του Πανεπιστημίου της Ουάσιγκτον ανακοίνωσαν πως δημιούργησαν στο εργαστήριο αρνητική μάζα</span></b></span></td></tr></tbody></table><p style="text-align: justify;"><span style="font-family: verdana; text-align: left;"><span style="font-family: verdana;"></span> Σύμφωνα με αυτήν την ανακάλυψη,η αρνητική μάζα βρίσκεται σε μία φάση της ύλης η οποία αποκαλείται συμπύκνωμα </span><b style="font-family: verdana; text-align: left;">Bose-Einstein </b><span style="font-family: verdana; text-align: left;">όπου τα επιμέρους σωματίδια κινούνται πολύ αργά εμφανίζοντας κυματική συμπεριφορά.</span><span style="font-family: verdana; text-align: left;">Επιπροσθέτως τα σωματίδια κινούνται σαν μία ολική οντότητα,ως ένα σωματίδιο,παρουσιάζοντας ιδιότητες υπερρευστού.</span><span style="font-family: verdana; text-align: left;">Σε αυτήν την κατάσταση,όπως προέβλεπαν οι<b> Satyendra Nath Bose</b> και <b>Albert Einstein</b>,τα σωματίδια κινούνται εξαιρετικά αργά και,ακολουθώντας τις αρχές της κβαντικής μηχανικής,συμπεριφέρονται σαν κύματα.</span><span style="font-family: verdana; text-align: left;">Συγχρονίζονται επίσης και κινούνται ταυτόχρονα ως αυτό που είναι γνωστό ως υπερρευστό,το οποίο ρέει χωρίς απώλεια ενέργειας.</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwZT1p8AGrrujvxEryBJ5UvzF5eYkERUu_bR5BD5gtx3lJOycPnfJX-G8psi-TlkF14Y4kCUGoehKeiJKfP2rRoLkLC7BGColyKDnXi2ymu-y1IWPVF_PYxxCljBEVR9BoP1mAFni2NLY/s1280/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259123.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="720" data-original-width="1280" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwZT1p8AGrrujvxEryBJ5UvzF5eYkERUu_bR5BD5gtx3lJOycPnfJX-G8psi-TlkF14Y4kCUGoehKeiJKfP2rRoLkLC7BGColyKDnXi2ymu-y1IWPVF_PYxxCljBEVR9BoP1mAFni2NLY/w640-h360/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259123.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="text-align: justify;"><b><span style="color: #800180; font-family: verdana;">Η αρνητική μάζα είναι μια υποθετική μορφή ύλης</span></b></span></td></tr></tbody></table><p></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: left;"> Με επικεφαλής τον<b> Peter Engels</b>,καθηγητή φυσικής και αστρονομίας του <b>WSU</b>,οι ερευνητές στον έκτο όροφο του <b>Webster Hall</b> δημιούργησαν αυτές τις συνθήκες χρησιμοποιώντας λέιζερ για να επιβραδύνουν τα σωματίδια,καθιστώντας τα πιο κρύα και επιτρέποντας σε θερμά,υψηλής ενέργειας σωματίδια να διαφύγουν σαν ατμός.</span><span style="font-family: verdana; text-align: left;">Τα λέιζερ παγιδεύτηκαν τα άτομα σαν να ήταν σε ένα "μπολ" με διαστάσεις μικρότερες από εκατό μικρά.</span><span style="font-family: verdana; text-align: left;">Σε αυτό το σημείο,το υπερρευστό ρουβίδιο έχει κανονική μάζα.</span><span style="font-family: verdana; text-align: left;">Το σπάσιμο του "μπολ" θα επιτρέψει στο ρουβίδιο να βγει έξω,να επεκταθεί καθώς το ρουβίδιο στο κέντρο ωθεί προς τα έξω.</span><span style="font-family: verdana; text-align: left;">Για να δημιουργήσουν αρνητική μάζα,οι ερευνητές εφάρμοσαν ένα δεύτερο σύνολο λέιζερ που κλωτσούσαν τα άτομα μπρος-πίσω και άλλαξαν τον τρόπο περιστροφής τους.</span><span style="font-family: verdana; text-align: left;">Τώρα όταν το ρουβίδιο εκτοξεύεται αρκετά γρήγορα,εάν συμπεριφέρεται σαν να έχει αρνητική μάζα.</span><span style="font-family: verdana; text-align: left;">Η τεχνική που χρησιμοποιείται από τους ερευνητές του <b>WSU</b> αποφεύγει ορισμένα από τα υποκείμενα ελαττώματα που είχαν συναντηθεί σε προηγούμενες προσπάθειες κατανόησης της αρνητικής μάζας.</span><span style="font-family: verdana; text-align: left;">Η έρευνά τους διευκρινίζει,όσον αφορά την αρνητική μάζα,παρόμοια συμπεριφορά που παρατηρείται σε άλλα συστήματα.</span><span style="font-family: verdana; text-align: left;">Αυτός ο αυξημένος έλεγχος δίνει στους ερευνητές ένα νέο εργαλείο για τη μηχανική πειραμάτων για τη μελέτη της ανάλογης φυσικής στην αστροφυσική,όπως τα αστέρια νετρονίων,και κοσμολογικά φαινόμενα όπως οι μαύρες τρύπες και η σκοτεινή ενέργεια,όπου τα πειράματα είναι αδύνατα.</span></p><p style="text-align: justify;"><b style="text-align: center;"><span style="color: red; font-family: verdana;">ΠΑΡΑΤΗΡΗΣΗ ΑΡΝΗΤΙΚΗΣ ΜΑΖΑΣ</span></b></p><p style="text-align: justify;"><span style="font-family: verdana;"><span style="text-align: center;"> Η ύπαρξη της αρνητικής μάζας δεν έχει επιβεβαιωθεί,αν και δεν παραβιάζει κανέναν νόμο της <b>Φυσικής</b>.Αν υπάρχει,που μπορούμε να βρούμε ποσότητες αρνητικής μάζας;</span><span style="text-align: center;">Ο <b>Robert Forward</b> αναφέρει πως ίσως να υπάρχει σε περιοχές του <b>Σύμπαντος </b>που ονομάζονται <b>Φυσαλίδες</b>,κενές περιοχές οι οποίες έχουν διάμετρο τουλάχιστον <b>100 εκατομμύρια έτη φωτός</b>.</span></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg34YAALXxaZLy4A67NYc0nT3zKe6RM8qOXhUQXQDUpFAZaQd4aJswgPr8CNIeQ5QG_2NSztJdZSc6cMgXmR6QjTC9bwStWyiI54dzrPb6OcjCDuWMlFKuF2Ksg2UE9fMc17A75P8mV8Qo/s505/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%25913.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="271" data-original-width="505" height="344" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg34YAALXxaZLy4A67NYc0nT3zKe6RM8qOXhUQXQDUpFAZaQd4aJswgPr8CNIeQ5QG_2NSztJdZSc6cMgXmR6QjTC9bwStWyiI54dzrPb6OcjCDuWMlFKuF2Ksg2UE9fMc17A75P8mV8Qo/w640-h344/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%25913.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="color: #800180;"><b><span style="font-family: verdana;">Ίσως να υπάρχει σε περιοχές του </span><span style="font-family: verdana;">Σύμπαντος </span><span style="font-family: verdana;">που ονομάζονται </span><span style="font-family: verdana;">Φυσαλίδες</span><span style="font-family: verdana;">,κενές περιοχές οι οποίες έχουν διάμετρο τουλάχιστον </span><span style="font-family: verdana;">100 εκατομμύρια έτη φωτός</span></b></span></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="font-family: verdana;"><span></span></span></div><p style="text-align: justify;"><span style="font-family: verdana; text-align: left;"><span style="font-family: verdana;"></span></span></p><div style="text-align: justify;"><span style="font-family: verdana;"><span style="text-align: center;"> Μία ομάδα επιστημόνων στην <b>Ρωσία </b>μελέτησε την πιθανότητα ύπαρξης σωματιδίων αρνητικής ύλης τα οποία έλκονται από τον <b>Ήλιο</b>.Αν όντως ίσχυε αυτό,τότε οι αλληλεπιδράσεις των σωματιδίων αρνητικής ύλης με τον <b>Ήλιο</b> θα τον έκανε να λάμπει για πάντα,κάτι το οποίο δεν ισχύει.</span><span style="text-align: center;">Ο φυσικός <b>Paul Wesson</b> προτείνει την ύπαρξη αρνητικής μάζας στο κέντρο μιας μαύρης τρύπας ή ενός άστρου νετρονίων καθώς καταρρέει.</span></span></div><p style="text-align: justify;"><span style="color: red; font-family: verdana;"><b>ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΣΤΟ ΔΕΥΤΕΡΟ ΝΟΜΟ ΤΟΥ ΝΕΥΤΩΝΑ</b></span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="color: #202122;"> </span>Ο <b>Ισαάκ Νεύτωνας</b> διατύπωσε <span style="background-color: transparent;">την παρακάτω εξίσωση</span><span style="background-color: transparent;"><span>,που συνδέει τ</span></span></span><span style="background-color: transparent; font-family: verdana;"><span style="text-align: start;">η δύναμη που ασκείται σε ένα σώμα,</span></span><span style="background-color: transparent; font-family: verdana;"><span style="line-height: 22px; text-indent: -24px;"><span face=""verdana" , sans-serif">τη </span></span><span style="text-align: left;">αδρανειακή </span><span style="line-height: 22px; text-indent: -24px;"><span face=""verdana" , sans-serif"><span>μάζα </span>του σώματος και τ</span></span></span><span style="background-color: transparent; font-family: verdana;"><span class="Apple-style-span" face=""verdana" , sans-serif" style="line-height: 22px; text-indent: -24px;">η <span>επιτάχυνση</span> που αποκτάει το σώμα από την επίδραση της </span><span face=""verdana" , sans-serif" style="line-height: 22px; text-indent: -24px;">δύναμης και</span></span><span style="background-color: transparent; font-family: verdana;"> λέγεται</span><span style="background-color: transparent; font-family: verdana;"> <span style="font-weight: bold;">θεμελιώδης νόμος της Μηχανικής</span><b> </b></span><span style="background-color: transparent; font-family: verdana;">ή <span style="font-weight: bold;">νόμος του Νεύτωνα</span></span><b style="background-color: transparent; font-family: verdana;">:</b></p><p style="background-color: white; color: #202122; margin: 0.5em 0px;"><span style="background-color: transparent; text-align: justify;"><span style="font-family: verdana;"><br /></span></span></p><div style="text-align: left;"><span style="font-family: verdana;"><img alt="{\vec {F}}=m{\vec {a}}" aria-hidden="true" class="mwe-math-fallback-image-inline" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7b202a8eaba4b424be52bcbaa043727b6ad9860" style="border: 0px; display: inline-block; height: 2.843ex; margin-left: auto; margin-right: auto; vertical-align: -0.338ex; width: 8.14ex;" /></span></div><p style="background-color: white; margin: 0.5em 0px;"><br /></p><div style="padding: 0px; text-align: justify;"><span style="background-color: white; color: #202122; text-align: left;"><span style="font-family: verdana;"> Τώρα θα πρέπει να μελετήσουμε τον <b>δεύτερο νόμο του Νεύτωνα</b> στην περίπτωση που η τιμή της μάζας είχε αρνητικό πρόσημο.Σε αυτό το σημείο ξεκινάνε και τα παράδοξα τις αρνητικής μάζας.<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDrQbGlQDfrhhVewsuvgoT3UMwUbGHsr5_lpc6ygG84p3AjAWTMT7fWJFKWJGYa8aX9xBJr2K7sHjGmwSyCfvTbNDSEWEb_F-LlZkRbfFx2jRg3PegQQ0mT84rTpoyeI5FskhhN9LeYnY/s800/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259125.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="480" data-original-width="800" height="384" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDrQbGlQDfrhhVewsuvgoT3UMwUbGHsr5_lpc6ygG84p3AjAWTMT7fWJFKWJGYa8aX9xBJr2K7sHjGmwSyCfvTbNDSEWEb_F-LlZkRbfFx2jRg3PegQQ0mT84rTpoyeI5FskhhN9LeYnY/w640-h384/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259125.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="color: #800180;"><b><span style="font-family: verdana; text-align: justify;">Αν σ</span><span style="font-family: verdana; text-align: justify;"><span style="background-color: transparent; text-align: left;">πρώξουμε μια αρνητική μάζα δεν επιταχύνεται προς την κατεύθυνση που ωθήθηκε,άλλα ε</span><span style="background-color: transparent; text-align: left;">πιταχύνει προς τα πίσω</span></span></b></span></td></tr></tbody></table><br /></span></span></div><div style="padding: 0px; text-align: justify;"><span style="background-color: white; color: #202122; text-align: left;"><span style="font-family: verdana;"> Σε αυτήν την περίπτωση ο <b>δεύτερος νόμος του Νεύτωνα</b> παίρνει την μορφή:</span></span></div><div style="padding: 0px; text-align: justify;"><span style="background-color: white; color: #202122; text-align: left;"><span style="font-family: verdana;"><br /></span></span></div><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"></dd></dl><div class="separator" style="clear: both; text-align: justify;"><span style="clear: left; float: left; font-family: verdana; margin-bottom: 1em; margin-right: 1em;"><img alt="{\vec {F}}=(-m){\vec {a}}" aria-hidden="true" class="mwe-math-fallback-image-inline" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60bfb51555f13837a26bb114f00a91d2b414e2c2" style="border: 0px; display: inline-block; height: 3.343ex; vertical-align: -0.838ex; width: 11.757ex;" /></span><span class="mwe-math-element" style="margin-left: 1em; margin-right: 1em;"></span></div><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> </span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Μπορούμε να παρατηρήσουμε ότι όταν ασκείται μια δύναμη σε ακίνητο σώμα αρνητικής μάζας <b>-m</b>,τότε το σώμα κινείται με επιτάχυνση αντίθετη με την κατεύθυνση της δύναμης.Αυτό σημαίνει πως αν σπρώξουμε ένα σώμα αρνητικής μάζας αυτό θα πλησιάζει προς το μέρος μας,και αν το τραβήξουμε προς το μέρος μας αυτό θα απομακρυνθεί.</span><span style="font-family: verdana;">Και βέβαια από μόνο του το γεγονός αυτό κάνει τον χειρισμό των σωμάτων με αρνητική μάζα αρκετά δύσκολο πως θα μπορούσαμε να πιάσουμε μια αρνητική μάζα.</span><span style="font-family: verdana;">Με απλά λόγια αν σ</span><span style="font-family: verdana;"><span style="background-color: transparent; text-align: left;">πρώξουμε μια αρνητική μάζα,σε αντίθεση με κάθε φυσικό αντικείμενο στον κόσμο που γνωρίζουμε,δεν επιταχύνεται προς την κατεύθυνση που ωθήθηκε,άλλα ε</span><span style="background-color: transparent; text-align: left;">πιταχύνει προς τα πίσω.</span></span></p><div><br style="font-family: verdana;" /></div><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><b style="color: red; font-family: verdana;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΚΑΙ ΘΕΤΙΚΗ ΜΑΖΑ</b></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"> Οι ομόσημες μάζες <b>θετική μάζα-θετική μάζα</b> ασκούν η μία στην άλλη ελκτικές βαρυτικές δυνάμεις.</span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj02hCrvt0rMvrtKIiKmq2EJiVMUqaZBdUS_H_jP88z0SyPiDQkieOmbpSNgtlFKBGHb4MEU6MXT65-AXWO2J77H4jRtUjmkN_uCXPpXeGRQOGRRf-buO3d715L5CzQLBxkaze2UeYj5iA/s446/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259110.jpg" style="margin-left: auto; margin-right: auto;"><span style="color: #800180;"><img border="0" data-original-height="294" data-original-width="446" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj02hCrvt0rMvrtKIiKmq2EJiVMUqaZBdUS_H_jP88z0SyPiDQkieOmbpSNgtlFKBGHb4MEU6MXT65-AXWO2J77H4jRtUjmkN_uCXPpXeGRQOGRRf-buO3d715L5CzQLBxkaze2UeYj5iA/s16000/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259110.jpg" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><span style="color: #800180; font-family: verdana;"><span style="text-align: justify;">Οι ομόσημες μάζες </span><span style="text-align: justify;">θετική μάζα-θετική μάζα </span></span></b></td></tr></tbody></table><p></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"> Επίσης οι ομόσημες μάζες αρνητική μάζα-αρνητική μάζα ασκούν η μία στην άλλη ελκτικές βαρυτικές δυνάμεις</span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhm9lXoU7rIEWuLbFCetPg26qoCGRCA0IfXrFdnfge97-L1hLQn4yNE3gHKnkgTbO3AfRaRve1esbu7KWdRKV6zijCFps1As404A5oLq5jrz6Nw9seanvyTUz9j66_vHqkRvy_aKHBwkJk/s448/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259111.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="296" data-original-width="448" height="264" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhm9lXoU7rIEWuLbFCetPg26qoCGRCA0IfXrFdnfge97-L1hLQn4yNE3gHKnkgTbO3AfRaRve1esbu7KWdRKV6zijCFps1As404A5oLq5jrz6Nw9seanvyTUz9j66_vHqkRvy_aKHBwkJk/w400-h264/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259111.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><span style="color: #800180; font-family: verdana;"><span style="text-align: justify;">Οι ομόσημες μάζες </span>αρνητική μάζα-αρνητική μάζα</span></b></td></tr></tbody></table><span style="color: #202122; font-family: verdana;"> Οι ετερόσημες μάζες θετική μάζα -αρνητική μάζα ασκούν η μία στην άλλη απωστικές βαρυτικές δυνάμεις.Πρέπει να επισημάνουμε ότι η διαφοροποίηση με την ηλεκτροστατική,όπου τα ομόσημα ηλεκτρικά φορτία απωθούνται,ενώ τα ετερόσημα έλκονται.</span><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><img border="0" data-original-height="292" data-original-width="452" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNbGbW-GtEGKWhvhQUMI-6J6mRil3_fxAiJ6XeJAB67rSvGDYlCUR2zfcm6UdBsnZTrHea7uT3ax-X38A1Xq232h9gIaJ9Cut0ky18AECmXz-fRf8WtGI0uRBv22Ve7DH1Y_kBt-nyXQw/s16000/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259112.jpg" style="margin-left: auto; margin-right: auto;" /></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="text-align: justify;"><span style="color: #800180; font-family: verdana;"><b>Οι ετερόσημες μάζες θετική μάζα -αρνητική μάζα ασκούν η μία στην άλλη απωστικές βαρυτικές δυνάμεις</b></span></span></td></tr></tbody></table><p></p><div style="text-align: justify;"><p style="background-color: white; margin: 0.5em 0px;"><span style="color: #202122; font-family: verdana;"> Οι δυο ετερόσημες μάζες,οι οποίες αρχικά ήταν ακίνητες,ασκούν η μία στην άλλη απωστικές δυνάμεις.Έτσι,η θετική μάζα επιταχύνεται προς την κατεύθυνση της δύναμης <b>F</b>,ενώ η αρνητική μάζα επιταχύνεται αντίθετα προς την κατεύθυνση της δύναμης <b>F’</b>:</span></p><p style="background-color: white; margin: 0.5em 0px;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGhM9ho14dikH9yGWB8ppeXcDZ3wcW_VxN44RvfSyhy6vAyQC34O2L661P_nF-xtSu0bE7xnWqocxxc8H6JnQ6vnJouKANXyfcHxQ03YAuUyc8xlaWhDCOwj-f3ENN3jdtKD_q80nbjb0/s312/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259115.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="113" data-original-width="312" height="145" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGhM9ho14dikH9yGWB8ppeXcDZ3wcW_VxN44RvfSyhy6vAyQC34O2L661P_nF-xtSu0bE7xnWqocxxc8H6JnQ6vnJouKANXyfcHxQ03YAuUyc8xlaWhDCOwj-f3ENN3jdtKD_q80nbjb0/w400-h145/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259115.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white; text-align: justify;"><span style="color: #800180; font-family: verdana;"><b>Οι δυο ετερόσημες μάζες του σχήματος, οι οποίες αρχικά ήταν ακίνητες,ασκούν η μία στην άλλη απωστικές δυνάμεις</b></span></span></td></tr></tbody></table><p style="background-color: white; margin: 0.5em 0px;"><span style="color: #202122; font-family: verdana;"><br /> Αν οι απόλυτες τιμές των μαζών είναι ίσες, τότε και οι επιταχύνσεις τους θα είναι ίσες.Συνεπώς,ενώ η απόσταση των δυο μαζών θα παραμένει σταθερή,το σύστημα θα επιταχύνεται συνεχώς προς τα δεξιά.</span></p></div><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px;"><b style="color: red; text-align: justify;"><span style="font-family: verdana;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΣΤΟΝ ΝΟΜΟ ΤΗΣ ΒΑΡΥΤΙΚΗΣ ΕΛΞΗΣ</span></b></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Επίσης,ο νόμος της βαρυτικής έλξης διατυπώνεται από την εξίσωση:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><b><span style="font-family: verdana;">F=G</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">m</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">M/d</span><span style="font-family: verdana;"><sup style="line-height: 19px;">2</sup></span></b></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><br /></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">όπου <i><b>F</b></i> η δύναμη που ασκείται μεταξύ δύο σωμάτων βαρυτικής μάζας <i><b>M</b> </i>και <i><b>m</b></i> από απόσταση <i><b>d</b></i> και <i><b>G</b></i> η σταθερά της παγκόσμιας έλξης.Και στις δύο περιπτώσεις η μάζα είναι θετική.</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdAfJRbZ2FnjKCXHl7uqYxOqLlcV7JCqexIPFoY7MPcF87kwk5YYCPoQRFw4kCYpeu2WXzeapxX6bWW_bCEa4CxkZH539d7b1CJ5dtAHgBGyGqK3fRgdsS4VRPANkGNuMWyrF0dAz2qX8/s687/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259117.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="687" data-original-width="500" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdAfJRbZ2FnjKCXHl7uqYxOqLlcV7JCqexIPFoY7MPcF87kwk5YYCPoQRFw4kCYpeu2WXzeapxX6bWW_bCEa4CxkZH539d7b1CJ5dtAHgBGyGqK3fRgdsS4VRPANkGNuMWyrF0dAz2qX8/w466-h640/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259117.png" width="466" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="color: #800180; font-family: verdana;"><b>Αλληλεπιδράσεις μαζών </b></span></td></tr></tbody></table><p></p><p></p><div class="separator" style="clear: both; text-align: center;"></div><p></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Με την εφαρμογή του τύπου:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><b style="font-family: "Times New Roman";"><span style="font-family: verdana;">F=G</span></b></span><b><span style="font-family: verdana;">·</span><span style="font-family: verdana;"><span style="font-family: "Times New Roman";"><span style="font-family: verdana;">(-m)</span></span></span><span style="font-family: verdana;">·</span></b><b><span style="font-family: verdana;">M/d</span><span style="font-family: verdana;"><sup style="line-height: 19px;">2</sup></span></b></p><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px; text-align: justify;"><span class="mwe-math-element"></span></dd></dl><p style="background-color: white; color: #202122; margin: 0.5em 0px;"></p><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><span style="font-family: verdana;">παρατηρούμε πως η δύναμη <i><b>F</b></i> έχει αντίθετη κατεύθυνση από τον πραγματικό τύπο,τείνοντας να απομακρύνει τα δύο σώματα και η δύναμη που ασκεί η μάζα <i><b>M</b></i> πάνω στην μάζα <i><b>-m</b></i> θα είναι απωστική.Ωστόσο σύμφωνα με τα συμπεράσματα του δεύτερου νόμου του <b>Νεύτωνα</b> αν ασκήσουμε μια απωστική δύναμη σε ένα σώμα αρνητικής μάζας,θα κινηθεί προς το μέρος μας.Έτσι ένα σώμα αρνητικής μάζας δεν θα απομακρυνθεί από τη<b> Γη</b> αλλά θα την πλησιάζει.<br /></span></div><span style="font-family: verdana;"><div style="text-align: justify;"> Στην περίπτωση:</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><b style="background-color: white; color: #202122; font-family: "Times New Roman";"><span style="font-family: verdana;">F=G</span></b><b><span style="background-color: white; color: #202122;">·</span><span style="background-color: white; color: #202122; font-family: "Times New Roman";"><span style="font-family: verdana;">(-M)</span></span><span style="background-color: white; color: #202122;">·</span></b><b style="background-color: white; color: #202122; font-family: "Times New Roman";"><span style="font-family: verdana;">m/d</span><span style="font-family: verdana;"><sup style="line-height: 19px;">2</sup></span></b></div><div style="text-align: justify;"><br /></div></span><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">η δύναμη<b> <i>F</i></b> έχει αρνητικό πρόσημο και το σώμα μάζας <i><b>m</b></i> θα απομακρύνεται από σώμα μάζας <i><b>-M</b></i>.</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"></p><span style="font-family: verdana;"> Αντίθετα,στην περίπτωση:</span><p></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><div style="text-align: justify;"><b style="background-color: white; color: #202122;"><span style="font-family: verdana;">F=G</span></b><b><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="background-color: white; color: #202122;"><span style="font-family: verdana;">(-M)</span></span><span style="background-color: white; color: #202122; font-family: verdana;">·</span></b><b style="background-color: white; color: #202122;"><span style="font-family: verdana;">(-m)/d</span><span style="font-family: verdana;"><sup style="line-height: 19px;">2</sup></span></b></div><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px; text-align: justify;"><span class="mwe-math-element"></span></dd></dl><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">η <i><b>F</b></i> έχει θετικό πρόσημο αλλά και πάλι θα έχουμε απομάκρυνση του σώματος μάζας <i><b>-m</b></i> από εκείνο με μάζα<b> <i>-M</i></b>.</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px;"><b style="color: red; text-align: justify;"><span style="font-family: verdana;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΣΤΗΝ ΟΡΜΗ</span></b></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Ο μαθηματικός τύπος που υπολογίζει την ορμή ενός κινούμενου σώματος και συνδέει τ</span><span style="font-family: verdana;">η μάζα και τ</span><span style="font-family: verdana;">η ταχύτητά </span><span style="font-family: verdana;">του σώματος</span><span style="font-family: verdana;"> </span><span style="font-family: verdana;">είναι:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><img alt="{\vec {p}}=m{\vec {u}}" aria-hidden="true" class="mwe-math-fallback-image-inline" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d5a7c2d25b49956ba3c149a878fd1efaeb0a975" style="border: 0px; display: inline-block; height: 2.676ex; margin-left: -0.089ex; vertical-align: -0.671ex; width: 7.883ex;" /></span><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px; text-align: justify;"><span class="mwe-math-element"></span></dd></dl><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Ας υποθέσουμε πως ισχύει ο τύπος:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"><span style="font-family: verdana;"><img alt="{\vec {p}}=(-m){\vec {u}}" aria-hidden="true" class="mwe-math-fallback-image-inline" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c9b8457fe430903196daadebbbb77ff7b4bbcc1" style="border: 0px; display: inline-block; height: 2.843ex; margin-left: -0.089ex; vertical-align: -0.838ex; width: 11.501ex;" /></span><span style="font-family: verdana;"><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"><span style="font-family: verdana;"><br /></span></dl></span><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px; text-align: justify;"><span class="mwe-math-element"></span></dd></dl><p style="background-color: white; color: #202122; margin: 0.5em 0px;"></p><div style="text-align: justify;"><span style="font-family: verdana;"> Τότε μία σφαίρα θετικής μάζας θα έλξει μια σφαίρα αρνητικής μάζας,ενώ αντίθετα η σφαίρα αρνητικής μάζας θα απωθεί την σφαίρα θετικής μάζας.Οι δυνάμεις πάνω στις σφαίρες θα βρίσκονται προς μια κατεύθυνση,όπως επίσης και οι επιταχύνσεις των σφαιρών.Τότε η σφαίρα αρνητικής μάζας θα κυνηγάει την σφαίρα θετικής μάζας και οι ταχύτητες τους θα αυξάνονται συνέχεια.</span></div><p></p><p style="background-color: white; color: #202122; font-size: 14px; margin: 0.5em 0px;"><b style="color: red; font-size: medium; text-align: justify;"><span style="font-family: verdana;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΣΤΗΝ ΕΝΕΡΓΕΙΑ</span></b></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Σύμφωνα με την <b>Αρχή Διατήρησης της Ενέργειας</b> η συνολική ενέργεια </span><span style="font-family: verdana;"><b>Ε</b></span><span style="font-family: verdana; font-size: x-small;"><b>ολ</b> </span><span style="font-family: verdana;">ενός συστήματος σωμάτων παραμένει σταθερή:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><b>Ε<span style="font-size: x-small;">ολ</span>=σταθ.</b></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><br /></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Επίσης γνωρίζουμε ότι η</span><span style="font-family: verdana;"> κινητική ενέργεια </span><b style="font-family: verdana;">Κ </b><span style="font-family: verdana;">μιας σφαίρας μάζας <b>m</b> που κινείται με ταχύτητα <b>υ </b>υπολογίζεται από τον τύπο:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><b>Κ=1/2</b></span><b><span style="font-family: verdana;">·</span><span style="font-family: verdana;"><span>m</span></span><span style="font-family: verdana;">·</span></b><b style="font-family: verdana;"><span>υ</span><sup style="line-height: 19px;">2</sup></b></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Στη περίπτωση </span><span style="background-color: transparent; font-family: verdana;">μίας σφαίρας θετικής μάζας και μίας σφαίρας αρνητικής μάζας,</span><span style="font-family: verdana;">οι δύο σφαίρες ήταν αρχικά ακίνητες.Η συνολική αρχική ενέργεια </span><b><span style="font-family: verdana;">Ε</span><span style="font-family: verdana; font-size: x-small;">αρχ. </span></b><span style="font-family: verdana;">των δύο σφαιρών είναι:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Ε<span style="font-size: x-small;">αρχ.</span>=Κ<span style="font-size: x-small;">αρχ.</span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="font-size: x-small;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Ε<span style="font-size: x-small;">αρχ.</span>=Κ<span style="font-size: x-small;">(</span></span><span style="font-size: x-small;"><span style="font-family: verdana;">+</span><span style="font-family: verdana;"><span>m)</span></span></span><span style="font-family: verdana; font-size: small;">αρχ.+</span><span style="background-color: transparent; font-family: verdana;">Κ<span style="font-size: x-small;">(</span></span><span style="background-color: transparent; font-size: x-small;"><span style="font-family: verdana;">-</span><span style="font-family: verdana;"><span>m)</span></span></span><span style="background-color: transparent; font-family: verdana; font-size: small;">αρχ.</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="font-size: x-small;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="background-color: transparent; font-family: verdana;">Ε<span style="font-size: x-small;">αρχ.</span>=1/2</span><span style="background-color: transparent;"><span style="font-family: verdana;">·(+</span><span style="font-family: verdana;"><span>m)</span></span><span style="font-family: verdana;">·</span></span><span style="background-color: transparent; font-family: verdana;"><span>υ</span><sup style="line-height: 19px;">2</sup></span><span style="background-color: transparent; font-family: verdana;">+1/2</span><span style="background-color: transparent; font-family: verdana;"><span style="font-family: verdana;">·(-</span><span style="font-family: verdana;"><span>m)</span></span><span style="font-family: verdana;">·</span></span><span style="background-color: transparent; font-family: verdana;"><span>υ</span><sup style="line-height: 19px;">2</sup></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Ε</span><span style="font-family: verdana; font-size: x-small;">αρχ.=</span><span style="background-color: transparent; font-family: verdana;">1/2</span><span style="background-color: transparent;"><span style="font-family: verdana;">·(+</span><span style="font-family: verdana;"><span>m)</span></span><span style="font-family: verdana;">·</span></span><span style="background-color: transparent; font-family: verdana;"><span>0</span><sup style="line-height: 19px;">2</sup></span><span style="background-color: transparent; font-family: verdana;">=1/2</span><span style="background-color: transparent; font-family: verdana;"><span style="font-family: verdana;">·(-</span><span style="font-family: verdana;"><span>m)</span></span><span style="font-family: verdana;">·</span></span><span style="background-color: transparent; font-family: verdana;"><span>0</span><sup style="line-height: 19px;">2</sup></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><br /></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Ε</span><span style="font-family: verdana; font-size: x-small;">αρχ.=</span><span style="font-family: verdana;">0+0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Ε</span><span style="font-family: verdana;"><span style="font-size: x-small;">αρχ.</span>=0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Άρα η συνολική αρχική ενέργεια του συστήματος είναι μηδέν.</span><span style="background-color: transparent; font-family: verdana; text-align: left;">Ύστερα λόγω της έλξης,οι δύο σφαίρες απέκτησαν και οι δύο κινητική ενέργεια.</span><span style="background-color: transparent; font-family: verdana; text-align: left;">Έτσι η σφαίρα με τη θετική μάζα απέκτησε θετική κινητική ενέργεια και η σφαίρα με την αρνητική μάζα απέκτησε αρνητική κινητική ενέργεια.</span><span style="background-color: transparent; font-family: verdana; text-align: left;">Η συνολική τελική ενέργεια </span><b style="background-color: transparent; text-align: left;"><span style="font-family: verdana;">Ε</span><span style="font-family: verdana; font-size: x-small;">τελ. </span></b><span style="background-color: transparent; font-family: verdana; text-align: left;">των δύο σφαιρών είναι:</span></p><p></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Ε<span style="background-color: transparent; font-family: "Times New Roman";"><span style="font-family: verdana; font-size: x-small;">τελ.</span></span>=Κ</span><span style="font-family: verdana; font-size: small;">τελ.</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="font-size: x-small;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Ε<span style="font-size: small;">τελ.</span>=Κ<span style="font-size: x-small;">(</span></span><span style="font-size: x-small;"><span style="font-family: verdana;">+</span><span style="font-family: verdana;"><span>m)</span></span></span><span style="font-family: verdana; font-size: small;">τελ.</span><span style="font-family: verdana; font-size: small;">+</span><span style="background-color: transparent; font-family: verdana;">Κ<span style="font-size: x-small;">(</span></span><span style="background-color: transparent; font-size: x-small;"><span style="font-family: verdana;">-</span><span style="font-family: verdana;"><span>m)</span></span></span><span style="font-family: verdana; font-size: small;">τελ.</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="font-size: x-small;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="background-color: transparent; font-family: verdana;">Ε<span style="font-size: small;">τελ.</span>=1/2</span><span style="background-color: transparent;"><span style="font-family: verdana;">·(+</span><span style="font-family: verdana;"><span>m)</span></span><span style="font-family: verdana;">·</span></span><span style="background-color: transparent; font-family: verdana;"><span>υ</span><sup style="line-height: 19px;">2</sup></span><span style="background-color: transparent; font-family: verdana;">+1/2</span><span style="background-color: transparent; font-family: verdana;"><span style="font-family: verdana;">·(-</span><span style="font-family: verdana;"><span>m)</span></span><span style="font-family: verdana;">·</span></span><span style="background-color: transparent; font-family: verdana;"><span>υ</span><sup style="line-height: 19px;">2</sup></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Ε</span><span style="font-family: verdana; font-size: small;">τελ.</span><span style="font-family: verdana; font-size: x-small;">=</span><span style="background-color: transparent; font-family: verdana;">1/2</span><span style="background-color: transparent;"><span style="font-family: verdana;">·(+</span><span style="font-family: verdana;"><span>m</span></span></span><span style="background-color: transparent; font-family: verdana;"><span style="font-family: verdana;">-</span><span style="font-family: verdana;"><span>m)</span></span><span style="font-family: verdana;">·</span></span><span style="font-family: verdana;">υ</span><sup style="font-family: verdana; line-height: 19px;">2</sup></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><br /></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Ε</span><span style="font-family: verdana;"><span style="font-size: small;">τελ.</span>=0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Άρα καταλήγουμε στο συμπέρασμα ότι η </span><span style="background-color: transparent; font-family: verdana;">συνολική αρχική ενέργεια </span><b><span style="font-family: verdana;">Ε</span><span style="font-family: verdana; font-size: x-small;">αρχ. </span></b><span style="font-family: verdana;">και η </span><span style="background-color: transparent; font-family: verdana;">συνολική τελική ενέργεια </span><span style="background-color: transparent;"><span style="font-family: verdana; font-weight: bold;">Ε</span><span style="font-family: verdana;"><b style="font-size: small;">τελ.</b> είναι ίσες</span></span><span style="background-color: transparent; font-family: verdana;">:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="background-color: transparent; font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><b><span style="font-family: verdana;">Ε</span><span style="font-family: verdana; font-size: x-small;">αρχ.=</span></b><span style="background-color: transparent;"><span style="font-family: verdana; font-weight: bold;">Ε</span><span style="font-family: verdana;"><b style="font-size: small;">τελ.</b></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="background-color: transparent; font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Συνεπώς η συνολική ενέργεια </span><span style="font-family: verdana;"><b>Ε</b></span><span style="font-family: verdana; font-size: x-small;"><b>ολ</b> </span><span style="font-family: verdana;">του συστήματος σωμάτων παραμένει σταθερή:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><b>Ε<span style="font-size: x-small;">ολ</span>=σταθ.</b></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><b><br /></b></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> </span><span style="font-family: verdana;">Έτσι συμπεραίνουμε ότι στην περίπτωση μας δεν παραβιάζεται η </span><b style="font-family: verdana;">Αρχή Διατήρησης της Ενέργειας</b><span style="font-family: verdana;">.</span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"><b style="color: red;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΚΑΙ ΓΗ</b></span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"> Θα προσπαθήσουμε να καταλάβουμε τι θα συμβεί αν καταφέρουμε να αφήσουμε μια αρνητική μάζα </span><b style="color: #202122; font-family: verdana;">-1 kg </b><span style="color: #202122; font-family: verdana;">να πέσει ελεύθερα στην επιφάνεια της <b>Γης.</b></span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"><b></b></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6-9UXK4c64BtknUZNm5Qfw_Mu25IW96v5W83rD9vF5TJBK7RTSqogcGEBJP4el_qEYz0cXBLGr_RIosN-N1MGdOTTQFJn1kZX5N6g61gw0mkjgxev-klGokCo_RiWOXUkxXcAKGI36NQ/s406/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259116.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="406" data-original-width="355" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6-9UXK4c64BtknUZNm5Qfw_Mu25IW96v5W83rD9vF5TJBK7RTSqogcGEBJP4el_qEYz0cXBLGr_RIosN-N1MGdOTTQFJn1kZX5N6g61gw0mkjgxev-klGokCo_RiWOXUkxXcAKGI36NQ/w350-h400/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259116.jpg" width="350" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><span style="color: #800180; font-family: verdana;"><span style="text-align: justify;">Η</span><span style="text-align: justify;"> Γη</span><span style="text-align: justify;"> έχει θετική μάζα,συνεπώς η αρνητική μάζα θα δεχτεί δύναμη με φορά προς τα πάνω</span></span></b></td></tr></tbody></table><p></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"> Η<b> Γη</b> έχει θετική μάζα,συνεπώς η αρνητική μάζα θα δεχτεί δύναμη με φορά προς τα πάνω.Όμως επειδή είναι αρνητική μάζα,θα επιταχυνθεί προς τα κάτω,αντίθετα με την φορά της δύναμης.Δηλαδή θα εκτελεί ελεύθερη πτώση,όπως και οι συνηθισμένες θετικές μάζες.</span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"><b style="color: red;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΚΑΙ ΝΗΜΑ </b></span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"> Θα προσπαθήσουμε να καταλάβουμε τι θα συμβεί αν καταφέρουμε να δέσουμε μια αρνητική μάζα με ένα νήμα και στο άλλο άκρο του νήματος εφαρμόζαμε μια δύναμη προς τα κάτω,μεγαλύτερη από το βάρος της.Τότε η αρνητική μάζα θα επιταχυνόταν προς τα πάνω.Αυτό μοιάζει με ένα παιδικό μπαλόνι,αλλά αν κοβόταν το νήμα ενώ το μπαλόνι θα έφευγε προς τα πάνω,η αρνητική μάζα θα έπεφτε προς τα κάτω.</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><img border="0" data-original-height="600" data-original-width="800" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio5cFt83iItWdKUp32NSs55iTebJeN8GXm3siZbd9DmV6nVwruyUIP0SNKL3IRFzndRRaNhaT4BnSYgaXIaRP2w4BIdFwobI5Bw8q-r9niEBIvJciHS51C-C-Md8pesjkD4MeHBwF2iRg/s320/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%25915.jpg" style="margin-left: auto; margin-right: auto;" width="320" /></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><span style="color: #800180;"><span style="background-color: white; font-family: verdana; text-align: justify;">Αν έχουμε αρνητική μάζα</span><span style="background-color: white; font-family: verdana; text-align: justify;"> -m</span><span style="background-color: white; font-family: verdana; text-align: justify;"> στο πάνω άκρο του αβαρούς νήματος και δέσουμε μάζα </span><span style="background-color: white; font-family: verdana; text-align: justify;">+m </span><span style="background-color: white; font-family: verdana; text-align: justify;">στο κάτω άκρο του νήματος τότε το σύστημα θα αιωρείται,αφού η συνολική μάζα είναι μηδέν</span></span></b></td></tr></tbody></table><p></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"> Αυτό γίνεται ακόμα πιο παράξενο να αντικαταστήσουμε την δύναμη του παιδιού στο νήμα με μια θετική μάζα.Αν π.χ. έχουμε αρνητική μάζα<b> -1 kg</b> στο πάνω άκρο του αβαρούς νήματος και δέσουμε μάζα <b>+1 kg </b>στο κάτω άκρο του νήματος τότε το σύστημα θα αιωρείται,αφού η συνολική μάζα είναι μηδέν.</span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"> <b>Και όταν το νήμα κοπεί τότε και οι δυο μάζες θα πέσουν προς τα κάτω.</b></span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: red; font-family: verdana;"><b>ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΚΑΙ ΕΛΑΤΗΡΙΟ </b></span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"></span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"> Τώρα πρέπει να σκεφτούμε τι θα συμβεί αν ένα σώμα με αρνητική μάζα <b>-m</b> δεθεί στο ένα άκρο ελατηρίου σταθεράς <b>k</b>,και απομακρυνθεί από την θέση ισορροπίας.Προφανώς δεν θα εκτελέσει απλή αρμονική ταλάντωση. </span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"> Η απομάκρυνση από την θέση ισορροπίας θα αυξάνεται εκθετικά με τον χρόνο: </span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"> </span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><b><span style="font-family: verdana;"><span>x(t)</span><span style="text-align: left;">~</span>e<sup style="line-height: 19px;">t</sup></span></b><b style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-align: left;"><span style="font-family: "Cambria Math", serif; line-height: 28px;"><span style="font-size: large;">√</span></span></b><b><span style="font-family: verdana;"><span lang="EN-GB" style="text-align: left;"> </span><sup style="line-height: 19px;">k/m</sup></span></b></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"><br /></span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;">και το σώμα θα επιταχύνεται συνεχώς τεντώνοντας το ελατήριο μέχρι να το σπάσει!</span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: red; font-family: verdana;"><b>ΑΔΡΑΝΕΙΑΚΗ ΚΑΙ ΒΑΡΥΤΙΚΗ ΜΑΖΑ</b></span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="color: #202122; font-family: verdana;"> Κατά την εξέταση της αρνητικής μάζας,είναι σημαντικό να εξετάσουμε ποιες από αυτές τις έννοιες της μάζας είναι αρνητικές.Από τότε που ο <b>Νεύτωνας </b>διατύπωσε για πρώτη φορά τη θεωρία του για τη βαρύτητα,υπήρξαν τουλάχιστον τρεις εννοιολογικά διακριτές ποσότητες που ονομάζονται μάζα:</span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="color: red; font-weight: bold;">α)</span><span style="color: #202122;"><b> Η αδρανειακή μάζα.</b>Είναι η μάζα<b> m </b>που εμφανίζεται στο<b> δεύτερο νόμο κίνησης του Νεύτωνα F=m</b></span></span><span style="color: #202122; font-family: verdana;"><b>·</b></span><b style="color: #202122; font-family: verdana;">α.</b></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><b><span style="color: red;">β)</span><span style="color: #202122;"> Η "ενεργήτική" βαρυτική μάζα.</span></b></span><span style="font-family: verdana;"><span style="color: #202122;">Είναι </span></span><span style="font-family: verdana;"><span style="color: #202122;">η μάζα που </span></span><span style="font-family: verdana;">ασκεί τη δύναμη </span><span style="background-color: transparent; font-family: verdana;">στον νόμο της παγκόσμιας έλξης</span><b style="font-family: verdana;"><span style="color: #202122;">.</span></b></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><b><span style="color: red;">γ)</span><span style="color: #202122;"> Η "παθητική" βαρυτική μάζα.</span></b><span style="color: #202122;">Είναι </span><span style="color: #202122;">η</span><span style="color: #202122;"> μάζα που </span>που δέχεται τη δύναμη </span><span style="font-family: verdana;">στον νόμο της παγκόσμιας έλξης</span><b style="font-family: verdana;"><span style="color: #202122;">.</span></b></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Στην καθιερωμένη φυσική τα τρία είδη των μαζών θεωρούνται ταυτόσημα.Άλλωστε δεν υπάρχει πειραματικό δεδομένο που να δείχνει κάποια διαφορά μεταξύ αυτών μαζών.</span><span style="color: #202122; font-family: verdana;">Ο νόμος της διατήρησης της ορμής απαιτεί η ενεργή και παθητική βαρυτική μάζα να είναι ίδια.Η αρχή της ισοδυναμίας του <b>Αϊνστάιν</b> υποδηλώνει ότι η αδρανειακή μάζα πρέπει να ισούται με την παθητική βαρυτική μάζα και όλα τα πειραματικά στοιχεία μέχρι σήμερα έχουν βρει ότι είναι,πράγματι,πάντα τα ίδια.</span><span style="color: #202122; font-family: verdana;">Στις περισσότερες αναλύσεις της αρνητικής μάζας,θεωρείται ότι η αρχή της ισοδυναμίας και η διατήρηση της ορμής συνεχίζουν να ισχύουν,και ως εκ τούτου και οι τρεις μορφές μάζας παραμένουν οι ίδιες,οδηγώντας στη μελέτη της </span><b style="color: #202122; font-family: verdana;">«αρνητικής μάζας»</b><span style="color: #202122; font-family: verdana;">.Όμως η αρχή της ισοδυναμίας είναι απλώς ένα παρατηρητικό γεγονός και δεν είναι απαραίτητα έγκυρο.Εάν γίνει μια τέτοια διάκριση,μια </span><b style="color: #202122; font-family: verdana;">"αρνητική μάζα" </b><span style="color: #202122; font-family: verdana;">μπορεί να είναι τριών ειδών,αν η αδρανειακή μάζα είναι αρνητική,η βαρυτική μάζα ή και τα δύο.</span></p><p style="text-align: justify;"><span style="font-family: verdana;"><span style="color: red; text-align: center;"><b>ΔΙΑΦΥΓΗΣ ΚΙΝΗΣΗ</b></span></span></p><p style="text-align: justify;"><span style="font-family: verdana;"><span style="text-align: center;"> Αν και κανένα σωματίδιο δεν είναι γνωστό ότι έχει αρνητική μάζα,οι φυσικοί <b>Hermann Bondi</b> το <b>1957</b>,ο<b> William B. Bonnor</b> το <b>1964 </b>και </span></span><span style="font-family: verdana; text-align: center;">ο <b>Robert L. Forward </b></span><span style="font-family: verdana;"><span style="text-align: center;">το <b>1989</b>,τότε ο <b>Robert L. Forward</b> μπόρεσαν να περιγράψουν μερικές από τις αναμενόμενες ιδιότητες που μπορεί να έχουν τέτοια σωματίδια.Υποθέτοντας ότι και οι τρεις έννοιες της μάζας είναι ισοδύναμες σύμφωνα με την αρχή της ισοδυναμίας,μπορούν να διερευνηθούν οι βαρυτικές αλληλεπιδράσεις μεταξύ μάζων αυθαίρετου σημείου,με βάση τη προσέγγιση των <b>Νευτώνιων εξισώσεων πεδίου του Αϊνστάιν</b>.</span></span></p><p style="text-align: justify;"><span style="font-family: verdana;"><span style="text-align: center;"> Οι νόμοι αλληλεπίδρασης είναι τότε:</span></span></p><p style="text-align: justify;"><span style="font-family: verdana;"><b><span style="color: red;">α)</span> Η θετική μάζα προσελκύει και τις άλλες θετικές μάζες και τις αρνητικές μάζες.</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"><b><span style="color: red;">β) </span>Η αρνητική μάζα απωθεί και τις άλλες αρνητικές μάζες και τις θετικές μάζες.</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"> Για δύο θετικές μάζες,τίποτα δεν αλλάζει και υπάρχει βαρυτική έλξη μεταξύ τους που προκαλεί έλξη.Δύο αρνητικές μάζες θα απωθούν λόγω των αρνητικών αδρανειακών μαζών τους.Ωστόσο,για διαφορετικά πρόσημα,υπάρχει μια ώθηση που απωθεί τη θετική μάζα από την αρνητική μάζα και μια έλξη που προσελκύει την αρνητική μάζα προς τη θετική ταυτόχρονα.</span><span style="font-family: verdana; text-align: center;">Ως εκ τούτου,ο <b>Bondi </b>επεσήμανε ότι δύο αντικείμενα ίσης και αντίθετης μάζας θα παρήγαγαν μια συνεχή επιτάχυνση του συστήματος προς το αντικείμενο θετικής μάζας,ένα αποτέλεσμα που ονομάζεται <b>"διαφυγής κίνηση"</b> από τον <b>Bonnor</b>,ο οποίος αγνόησε τη φυσική του ύπαρξη, δηλώνοντας:</span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"><br /></span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"><b>"Θεωρώ ότι η διαφυγής (ή αυτοεπιταχυνόμενη) κίνηση […] είναι τόσο παράλογη που προτιμώ να την αποκλείσω υποθέτοντας ότι η αδρανειακή μάζα είναι θετική ή αρνητική."</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"><br /></span></p><p style="text-align: justify;"><span style="color: #800180; font-family: verdana; text-align: center;"><b>- William B. Bonnor</b></span></p><p style="text-align: justify;"><span style="color: #274e13; font-family: verdana; text-align: center;"><b>για την αρνητική μάζα στη γενική σχετικότητα</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"> Ένα τέτοιο ζευγάρι αντικειμένων θα επιταχύνθηκε χωρίς όριο (εκτός από σχετικιστικό).Ωστόσο, η συνολική μάζα,ορμή και ενέργεια του συστήματος θα παραμείνει μηδέν.Αυτή η συμπεριφορά είναι εντελώς ασυνεπής με μια κοινή λογική προσέγγιση και την αναμενόμενη συμπεριφορά της «φυσιολογικής» ύλης.Ο <b>Thomas Gold </b>υπαινίχθηκε ακόμη ότι η γραμμική κίνηση της διαφυγής θα μπορούσε να χρησιμοποιηθεί σε μια μηχανή αέναης κίνησης εάν μετατραπεί σε κυκλική κίνηση:</span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"><br /></span></p><p style="text-align: justify;"><b><span style="font-family: verdana; text-align: center;">"Τι συμβαίνει εάν κάπ</span><span style="font-family: verdana; text-align: center;">οιος συνδέσει αρνητικό και θετικό ζεύγος μάζας στο χείλος ενός τροχού;Αυτό δεν είναι συμβατό με τη γενική σχετικότητα,γιατί η συσκευή γίνεται πιο μαζική."</span></b></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"><br /></span></p><p style="text-align: justify;"><span style="color: #2b00fe; font-family: verdana; text-align: center;"><b>- Thomas Gold</b></span></p><p style="text-align: justify;"><span style="color: #274e13; font-family: verdana; text-align: center;"><b><span>για την αρνητική μάζα στη γενική σχετικότητα</span> </b></span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"> Αλλά ο <b>Forward</b> έδειξε ότι το φαινόμενο είναι μαθηματικά συνεπές και δεν εισάγει παραβίαση των νόμων περί διατήρησης.Εάν οι μάζες είναι ίσες σε μέγεθος αλλά αντίθετες σε πρόσημο,τότε η ορμή του συστήματος παραμένει μηδέν εάν και οι δύο ταξιδεύουν μαζί και επιταχύνονται μαζί,ανεξάρτητα από την ταχύτητα τους:</span></p><p style="text-align: justify;"><b><span style="font-family: verdana; text-align: center;">p<span style="font-size: x-small;">ολ</span>=m</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="font-family: verdana; text-align: center;">υ+(-m</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="font-family: verdana; text-align: center;">υ)=[m+(-m)]</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="font-family: verdana; text-align: center;">υ=0</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="font-family: verdana; text-align: center;">υ=0</span></b></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"> Και ισοδύναμα για την κινητική ενέργεια:</span></p><p style="text-align: justify;"><b><span style="font-family: verdana; text-align: center;">Κ<span style="font-size: x-small;">ολ</span>=</span><span style="background-color: white; color: #202122; font-family: verdana;">1/2</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="background-color: white; color: #202122; font-family: verdana;">m</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="background-color: white; color: #202122; font-family: verdana;">υ</span><sup style="background-color: white; color: #202122; font-family: verdana; line-height: 19px;">2</sup><span style="background-color: white; color: #202122; font-family: verdana;">+1/2</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="background-color: white; color: #202122; font-family: verdana;">(-m)</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="background-color: white; color: #202122; font-family: verdana;">υ</span><sup style="background-color: white; color: #202122; font-family: verdana; line-height: 19px;">2</sup><span style="background-color: white; color: #202122; font-family: verdana;">=1/2</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="background-color: white; color: #202122; font-family: verdana;">[m</span><span style="background-color: white; color: #202122; font-family: verdana;">+(-m)]</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="background-color: white; color: #202122; font-family: verdana;">υ</span><sup style="background-color: white; color: #202122; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana; text-align: center;">=1/2</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="font-family: verdana; text-align: center;">(0)</span><span style="background-color: white; color: #202122; font-family: verdana;">·</span><span style="background-color: white; color: #202122; font-family: verdana;">υ</span><sup style="background-color: white; color: #202122; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana; text-align: center;">=0</span></b></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"> Ω</span><span style="font-family: verdana; text-align: center;">στόσο,αυτό ίσως δεν ισχύει ακριβώς εάν ληφθεί υπόψη η ενέργεια στο βαρυτικό πεδίο.</span><span style="font-family: verdana; text-align: center;">Ο <b>Forward</b> επέκτεινε την ανάλυση του <b>Bondi</b> σε πρόσθετες περιπτώσεις,και έδειξε ότι ακόμη και αν οι δύο μάζες <b>-m</b> και <b>+m</b> δεν είναι οι ίδιες,οι νόμοι διατήρησης παραμένουν αμετάβλητοι.Αυτό ισχύει ακόμη και όταν λαμβάνονται υπόψη οι σχετικιστικές επιδράσεις,εφόσον η αδρανειακή μάζα,όχι η μάζα ηρεμίας,είναι ίση με τη βαρυτική μάζα.</span><span style="font-family: verdana; text-align: center;">Αυτή η συμπεριφορά μπορεί να παράγει περίεργα αποτελέσματα,για παράδειγμα,ένα αέριο που περιέχει ένα μίγμα θετικών και αρνητικών </span><span style="font-family: verdana; text-align: center;">σωματιδίων</span><span style="font-family: verdana; text-align: center;"> θα έχει θετική αύξηση θερμοκρασίας.Ωστόσο,το τμήμα της αρνητικής ύλης αποκτά αρνητική θερμοκρασία στον ίδιο ρυθμό,εξισορροπώντας ξανά.Ο <b>Geoffrey A. Landis</b> επεσήμανε άλλες επιπτώσεις της ανάλυσης του <b>Forward</b>,συμπεριλαμβανομένης της σημείωσης ότι αν και τα αρνητικά σωματίδια μάζας θα απωθήσουν το ένα το άλλο βαρυτικά,η ηλεκτροστατική δύναμη θα ήταν ελκτική για παρόμοια φορτία και απωθητική για αντίθετα φορτία.</span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwVjLcqmFotR6pImrwo4o_Y_ZWha_dsgVyu8jFV-7NNHQIULhMrl-yNo5t4nGUqypzE20VIczby1OzQlS8CkUWMWWCfN3bl6OnYawnCOsWTII1Us-bJJqcQMfDWoQPKkxhCwepnK5LrPY/s200/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%25919.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="121" data-original-width="200" height="194" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwVjLcqmFotR6pImrwo4o_Y_ZWha_dsgVyu8jFV-7NNHQIULhMrl-yNo5t4nGUqypzE20VIczby1OzQlS8CkUWMWWCfN3bl6OnYawnCOsWTII1Us-bJJqcQMfDWoQPKkxhCwepnK5LrPY/w320-h194/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%25919.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white;"><span style="color: #800180; font-family: verdana;"><b><span style="text-align: left; vertical-align: inherit;"><span style="vertical-align: inherit;">Με κίτρινο χρώμα,η «παράλογη» </span></span><span style="text-align: left;"><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">διαφυγή κίνηση</span></span></span><span style="text-align: left; vertical-align: inherit;"><span style="vertical-align: inherit;"> θετικών και αρνητικών μαζών που περιγράφεται από τους Bondi και Bonnor</span></span></b></span></span></td></tr></tbody></table><p></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"> Ο <b>Forward </b>χρησιμοποίησε τις ιδιότητες της ύλης αρνητικής μάζας για να δημιουργήσει την έννοια της διαμετρικής κίνησης,ένα σχέδιο για πρόωση διαστημικού σκάφους που χρησιμοποιεί αρνητική μάζα που δεν απαιτεί είσοδο ενέργειας και καμία μάζα αντίδρασης για να επιτύχει αυθαίρετα υψηλή επιτάχυνση.</span><span style="font-family: verdana; text-align: center;">Ο<b> Forward</b> επινόησε επίσης έναν όρο,<b>"nullification"</b>,για να περιγράψει τι συμβαίνει όταν συναντώνται η ύλη και η αντιύλη.Αναμένεται να είναι σε θέση να ακυρώσουν την ύπαρξη του άλλου.Μια αλληλεπίδραση μεταξύ ίσων ποσοτήτων ύλης θετικής μάζας με θετική ενέργειας <b>E=m</b></span><span style="background-color: white; color: #202122; font-family: verdana;"><b>·</b></span><b><span style="color: #202122; font-family: verdana;">c</span><sup style="color: #202122; font-family: verdana; line-height: 19px;">2</sup></b><span style="font-family: verdana; text-align: center;"> και της ύλης αρνητικής μάζας με αρνητική ενέργεια <b>-E=-m</b></span><span style="background-color: white; color: #202122; font-family: verdana;"><b>·</b></span><b><span style="color: #202122; font-family: verdana;">c</span><sup style="color: #202122; font-family: verdana; line-height: 19px;">2</sup></b><span style="font-family: verdana; text-align: center;">,δεν απελευθερώνει ενέργεια,αλλά επειδή η μόνη διαμόρφωση τέτοιων σωματιδίων που έχει μηδέν ορμή (και τα δύο σωματίδια κινούνται με την ίδια ταχύτητα στην ίδια κατεύθυνση) δεν παράγουν σύγκρουση,τέτοιες αλληλεπιδράσεις θα αφήσουν ένα πλεόνασμα ορμής.</span></p><p style="text-align: justify;"><b><span style="color: red;"><span style="font-family: verdana;"><span style="text-align: center;">ΔΙΜΕΤΡΙΚΗ ΛΥΣΗ ΓΙΑ ΤΟ ΠΑΡΑΔΟΞΟ ΤΗΣ </span></span><span style="font-family: verdana; text-align: center;">ΔΙΑΦΥΓΗΣ ΚΙΝΗΣΗΣ</span></span></b></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"></span></p><p style="text-align: justify;"><span style="font-family: verdana;"><span style="text-align: center;"> Ο <b>Jean-Pierre Petit</b>,μ</span></span><span style="font-family: verdana; text-align: center;">έσω της διμετρικής προσέγγισης του <b>Νεύτωνα</b>,</span><span style="font-family: verdana; text-align: center;">πρότεινε μια λύση για το παράδοξο της διαφυγής κίνησης στην οποία:</span></p><p style="text-align: justify;"><b><span style="font-family: verdana; text-align: center;"><span style="color: red;">α)</span> </span><span style="font-family: verdana; text-align: center;">Όπως οι μάζες προσελκύουν,δηλαδή όπως η θετική μάζα προσελκύει τη θετική μάζα,έτσι και η αρνητική μάζα προσελκύει την αρνητική μάζα.</span></b></p><p style="text-align: justify;"><b><span style="font-family: verdana; text-align: center;"><span style="color: red;">β)</span> Οι αντίθετες </span><span style="font-family: verdana; text-align: center;">μάζες απωθούνται,δηλαδή η θετική μάζα και η αρνητική μάζα απωθεί η μια την άλλη.</span></b></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><img border="0" data-original-height="125" data-original-width="200" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYlgJJ3Ig2lPv5taqiA3Unw-yOHRcsk7grik0qj10snpwaQLe2zKqbKo2dNWPkQ-zPpqbdc-x7otzBDZArjs5xEWMF4ZhDpj1nozgkXUZShHeld-qWKysINil4V-U4YO_7YFxreFG-fFw/w320-h200/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%25917.jpg" style="margin-left: auto; margin-right: auto;" width="320" /></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white; text-align: left;"><span style="color: #800180; font-family: verdana;"><b>Στο πράσινο,οι βαρυτικές αλληλεπιδράσεις στις διμετρικές θεωρίες που διαφέρουν από αυτές που επεξεργάστηκαν οι Bondi και Bonnor,επιλύοντας το παράδοξο</b></span></span></td></tr></tbody></table><p></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"> Αν και τα μαθηματικά δεν είναι εύκολα,η δυναμική του συστήματος μπορεί να παρουσιαστεί χρησιμοποιώντας την ακόλουθη απλοποίηση (από την άποψη της </span><span style="font-family: verdana; text-align: center;">θετική </span><span style="font-family: verdana; text-align: center;">μάζας:</span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"><b><span style="color: red;">α)</span> Δύο θετικές μάζες ασκούν δύναμη μεταξύ τους που δείχνει προς τα μέσα και και οι δύο μάζες θα αντιδράσουν σε αυτήν επιταχύνοντας προς τα μέσα,δηλαδή ο νόμος της βαρύτητας με τον οποίο γνωρίζουμε.</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"><b><span style="color: red;">β)</span> Δύο αρνητικές μάζες ασκούν δύναμη μεταξύ τους που δείχνει προς τα έξω,αλλά και οι δύο μάζες,που είναι αρνητικές,θα αντιδρούν σε αυτήν επιταχύνοντας προς τα μέσα.Το τελικό αποτέλεσμα θα διακρίνεται από τον νόμο του Νεύτωνα με τον οποίο γνωρίζουμε.</b></span></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"><b><span style="color: red;">γ)</span> </b></span><span style="font-family: verdana; text-align: center;"><b>Μεταξύ θετικής και αρνητικής μάζας,η θετική μάζα ασκεί δύναμη στην αρνητική μάζα που δείχνει προς τα μέσα,αλλά η αρνητική μάζα θα αντιδράσει επιταχύνοντας προς τα έξω.</b>Από την άλλη πλευρά,η αρνητική μάζα ασκεί δύναμη στη θετική μάζα που δείχνει προς τα έξω και αυτό αντιδρά ανάλογα με την επιτάχυνση προς τα έξω.Το τελικό αποτέλεσμα θα εμφανιστεί ως συμμετρική απωθητική δύναμη μεταξύ των δύο αντίθετων μαζών (ένας <b>«νόμος αντίθετος του Νεύτωνα»</b>).</span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><img border="0" data-original-height="121" data-original-width="200" height="194" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfI0sg_pM_Sq8Zvy5PuIwWYv2rq_pI8RU2z9nhk7EFIPa-LV9XYCDreNy14XVDP75xSFbKhtc248sQMPDJTatId5tHkmz78X7ivU2l-wWuGMu09q_0GYZ1BpX8cjLt_-URVNXa2MZvZHM/w320-h194/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%25918.jpg" style="margin-left: auto; margin-right: auto;" width="320" /></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white;"><span style="color: #800180; font-family: verdana;"><b><span style="text-align: left; vertical-align: inherit;"><span style="vertical-align: inherit;">Μια πιθανή ερμηνεία της διμετρικής λύσης από </span></span><span style="text-align: left;"><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">την άποψη της θετικής μάζας.Σ</span></span></span><span style="text-align: left; vertical-align: inherit;"><span style="vertical-align: inherit;">ε διαφανές μπλε είναι η δύναμη που δέχεται η κάθε μάζα,στο αδιαφανές μπλε είναι το πώς αντιδρά το τελευταίο σε αυτήν</span></span></b></span></span></td></tr></tbody></table><p></p><p style="text-align: justify;"><span style="font-family: verdana; text-align: center;"> Αυτοί οι νόμοι είναι διαφορετικοί από τους νόμους που περιγράφονται από τους <b>Bondi</b> και <b>Bonnor</b> και επιλύουν το παράδοξο.</span><span style="font-family: verdana; text-align: center;">Για να γίνει αυτό,αναφέρονται στο κοσμολογικό <b>μοντέλο Janus</b> που αναπτύχθηκε από τον <b>Petit</b>,όπου η βαρύτητα θα μπορούσε να περιγραφεί από ένα διμετρικό μοντέλο που θα επέκτεινε τη γενική σχετικότητα.</span><span style="font-family: verdana; text-align: center;">Βελτιώθηκε το <b>2015 </b>για να δικαιολογήσει την επιτάχυνση της επέκτασης του σύμπαντος.Η έκδοση του <b>2014 (και 22 Νοεμβρίου 2016)</b> του μοντέλου επικρίθηκε από τον φυσικό <b>Thibault Damour</b> σε μια ανάλυση της <b>4ης Ιανουαρίου 2019</b>,η οποία κατέδειξε τη εσωτερική ασυνέπεια στο μοντέλο.Έκτοτε,έγιναν περαιτέρω αλλαγές στο μοντέλο,σε άρθρο που δημοσιεύθηκε αργότερα τον <b>Ιανουάριο</b> του <b>2019</b>.</span><span style="font-family: verdana; text-align: center;">Το έργο του <b>Petit </b>σε αυτό το θέμα δεν είχε μεγάλη απήχηση στους κοσμολόγους.Ωστόσο,ανεξάρτητες μελέτες διμετρικής βαρύτητας με θετικές και αρνητικές μάζες οδήγησαν στα ίδια συμπεράσματα σχετικά με τους νόμους της βαρύτητας.Κατά συνέπεια,η <b>NASA</b> εξετάζει τις επιπτώσεις της αρνητικής μάζας για ταχύτερη από την ελαφριά πρόωση ή τις σκουληκότρυπες.</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><b style="color: red;"><span style="font-family: verdana;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΣΤΗΝ ΕΙΔΙΚΗ ΘΕΩΡΙΑ ΤΗΣ ΣΧΕΤΙΚΟΤΗΤΑΣ</span></b></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"> Η αρνητική μάζα θα είχε κάποιες παράξενες ιδιότητες,όπως η επιτάχυνση στην αντίθετη κατεύθυνση της εφαρμοζόμενης </span>δύναμης<span style="vertical-align: inherit;"><span style="vertical-align: inherit;">.</span><span style="vertical-align: inherit;">Παρά το γεγονός ότι δεν είναι συνεπής με την αναμενόμενη συμπεριφορά της <b>«κανονικής»</b> ύλης,η αρνητική μάζα είναι μαθηματικά συνεπής και δεν εισάγει καμία παραβίαση της </span></span>διατήρησης της ορμής<span style="vertical-align: inherit;"> ή της </span>ενέργειας<span style="vertical-align: inherit;"><span style="vertical-align: inherit;">.</span><span style="vertical-align: inherit;">Χρησιμοποιείται σε ορισμένες θεωρητικές θεωρίες,όπως στην κατασκευή τεχνητών </span></span>σκουληκότρυπων<span style="vertical-align: inherit;"> και του </span>δίσκου <b>Alcubierre</b><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">.</span><span style="vertical-align: inherit;">Ο πλησιέστερος γνωστός πραγματικός αντιπρόσωπος μιας τέτοιας εξωτικής ύλης είναι η περιοχή της ψευδο</span></span>-αρνητικής πίεσης που<span style="vertical-align: inherit;"> παράγεται από την </span>επίδραση <b>Casimir</b><span style="vertical-align: inherit;">.</span><span style="vertical-align: inherit;">Σύμφωνα με </span>την ισοδυναμία μάζας-ενέργειας<span style="vertical-align: inherit;">,η μάζα <b>m</b></span><span style="vertical-align: inherit;"><b> </b>είναι ανάλογη με την ενέργεια<b> E</b></span><span style="vertical-align: inherit;"> και ο συντελεστής της αναλογικότητας είναι <b>c</b></span></span><sup style="font-family: verdana; line-height: 19px;"><b>2</b></sup><span style="font-family: verdana; vertical-align: inherit;">.</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjie5hZeF64JmaJtsj_Ru-ozUsjdZjLcTnbHKg9hUokaLKyjxTLr6tYyNFu8-ucQto3n8QhHLryvTdGrv2UPMYe3SiBme0xuJXIxRqx5oyJCk-4Iv5_U32wcq92qVc09E3sAU2z-fDwBTk/s412/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%25914.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="338" data-original-width="412" height="329" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjie5hZeF64JmaJtsj_Ru-ozUsjdZjLcTnbHKg9hUokaLKyjxTLr6tYyNFu8-ucQto3n8QhHLryvTdGrv2UPMYe3SiBme0xuJXIxRqx5oyJCk-4Iv5_U32wcq92qVc09E3sAU2z-fDwBTk/w400-h329/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%25914.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="color: #800180; font-family: verdana;"><b>Η θετική και αρνητική μάζα στη γενική θεωρία της σχετικότητας<br /></b></span></td></tr></tbody></table><span style="font-family: verdana;"><div style="text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"> Πράγματι,</span><span style="vertical-align: inherit;">η μάζα <b>m</b> εξακολουθεί να ισοδυναμεί με <b>E</b>,</span><span style="vertical-align: inherit;">αν και ο συντελεστής είναι μια άλλη σταθερά </span><span style="vertical-align: inherit;"> όπως <b>-</b></span></span><b><span style="font-family: verdana;">c</span><sup style="line-height: 19px;">2</sup></b><span style="font-family: verdana; vertical-align: inherit;">.</span><span style="font-family: verdana; vertical-align: inherit;">Σε αυτήν την περίπτωση,δεν είναι απαραίτητο να εισαχθεί μια </span><span style="font-family: verdana;">αρνητική ενέργεια,</span><span style="font-family: verdana; vertical-align: inherit;">επειδή η μάζα μπορεί να είναι αρνητική αν και η ενέργεια είναι θετική.</span></div></span><p></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;"> Δηλαδή:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;">E=-m</span><span style="font-family: verdana;">·</span><span style="background-color: transparent; font-family: verdana;">c</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana;">>0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">m=-E/</span><span style="background-color: transparent; font-family: verdana;">c</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana;"><0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;">Σε αυτή την περίπτωση:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;">dE=F</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">ds=dp/dt </span><span style="font-family: verdana;">· </span><span style="font-family: verdana;">ds=ds/dt </span><span style="font-family: verdana;">· </span><span style="font-family: verdana;">dp=υ</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">dp=υ</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">d(m</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">υ)</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;">-</span><span style="background-color: transparent; font-family: verdana;">c</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana;">·d</span><span style="font-family: verdana;">m=υ</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">d(m</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">υ)</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="background-color: transparent; font-family: verdana; vertical-align: inherit;">-</span><span style="background-color: transparent; font-family: verdana;">c</span><sup style="background-color: transparent; line-height: 19px;">2</sup><span style="background-color: transparent;">·</span>2m</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">dm=2m</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">υ</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">d(m</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">υ)</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="background-color: transparent; font-family: verdana; vertical-align: inherit;">-</span><span style="background-color: transparent; font-family: verdana;">c</span><sup style="background-color: transparent; line-height: 19px;">2</sup><span style="background-color: transparent;">·</span>d(m</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana;">)=d(</span><span style="background-color: transparent; font-family: verdana;">m<sup style="background-color: transparent; line-height: 19px;">2</sup></span><span style="font-family: verdana;">·υ</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana;">)</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;">-</span><span style="background-color: transparent; font-family: verdana;">m<sup style="background-color: transparent; line-height: 19px;">2</sup></span><span style="font-family: verdana;">·c<sup style="background-color: transparent; line-height: 19px;">2</sup>=</span><span style="font-family: verdana;"><span style="background-color: transparent; font-family: verdana;">m<sup style="background-color: transparent; line-height: 19px;">2</sup></span>·υ<sup style="background-color: transparent; line-height: 19px;">2</sup>+C</span></p><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px; text-align: justify;"><span class="mwe-math-element"></span></dd><dd style="margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px; text-align: justify;"><span class="mwe-math-element"><span style="font-family: verdana;"><br /></span></span></dd></dl><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Όταν:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">υ=0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">C=</span><span style="background-color: transparent; font-family: verdana; vertical-align: inherit;">-m<span style="font-size: x-small;">0</span></span><span style="background-color: transparent; font-family: verdana;"><sup style="line-height: 19px;">2</sup></span><span style="font-family: verdana;">·c<sup style="background-color: transparent; line-height: 19px;">2</sup> </span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;"> Συνεπώς:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;"><span style="font-family: verdana; vertical-align: inherit;">-</span><span style="background-color: transparent; font-family: verdana;">m<sup style="background-color: transparent; line-height: 19px;">2</sup></span>·c<sup style="background-color: transparent; line-height: 19px;">2</sup>=<span style="background-color: transparent; font-family: verdana;">m<sup style="background-color: transparent; line-height: 19px;">2</sup></span></span><span style="font-family: verdana;">·υ</span><span style="font-family: verdana; vertical-align: inherit;"><sup style="background-color: transparent; line-height: 19px;">2</sup></span><span style="background-color: transparent; font-family: verdana; vertical-align: inherit;">-m<span style="font-size: x-small;">0</span></span><span style="background-color: transparent; font-family: verdana;"><sup style="line-height: 19px;">2</sup></span><span style="font-family: verdana;">·c</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><br /></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">m=</span><span style="font-family: verdana;">m</span><span style="font-family: verdana; font-size: x-small;">0</span><span style="font-family: verdana; font-size: large;">/</span><span style="font-family: verdana;">(1+<span style="background-color: transparent; font-family: verdana;">υ</span><sup style="background-color: transparent; line-height: 19px;">2</sup>/<span style="background-color: transparent; font-family: verdana;">c</span><sup style="background-color: transparent; line-height: 19px;">2</sup>)</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">1/2</sup></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">όπου: </span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">m<span style="font-size: x-small;">0</span><0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">είναι </span>αναλλοίωτη μάζα<span style="vertical-align: inherit;"> και η </span>αμετάβλητη ενέργεια<span style="vertical-align: inherit;"> ισούται με:</span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;">E<span style="font-size: x-small;">0</span>=-</span><span style="background-color: transparent; font-family: verdana;">m<span style="font-size: x-small;">0</span></span><span style="font-family: verdana;">·c<sup style="background-color: transparent; line-height: 19px;">2</sup>>0</span><span style="font-family: verdana;"> </span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Η τετραγωνική μάζα είναι ακόμη θετική και το σωματίδιο μπορεί να είναι σταθερό.</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">Από:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="font-family: verdana;">m=</span>m<span style="font-size: x-small;">0</span><span style="font-size: large;">/</span>(1+<span style="background-color: transparent; font-family: verdana;">υ</span><sup style="background-color: transparent; line-height: 19px;">2</sup>/<span style="background-color: transparent; font-family: verdana;">c</span><sup style="background-color: transparent; line-height: 19px;">2</sup>)<sup style="background-color: transparent; line-height: 19px;">1/2</sup></span><span style="font-family: verdana;"><0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><br /></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">p=</span><span style="font-family: verdana;">m</span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">υ=</span><span style="background-color: transparent; font-family: verdana;">m<span style="font-size: x-small;">0</span><span style="font-size: large;">/</span>(1+<span style="font-family: verdana;">υ</span><sup style="line-height: 19px;">2</sup>/<span style="font-family: verdana;">c</span><sup style="line-height: 19px;">2</sup>)<sup style="line-height: 19px;">1/2</sup></span><span style="background-color: transparent; font-family: verdana;"><0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><br /></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"> Η </span>αρνητική ορμή<span style="vertical-align: inherit;"> εφαρμόζεται για να εξηγήσει την </span>αρνητική διάθλαση<span style="vertical-align: inherit;">,το </span>αντίστροφο <b>φαινόμενο Doppler</b><span style="vertical-align: inherit;"> και το </span>αντίστροφο <b>φαινόμενο Cherenkov</b> που<span style="vertical-align: inherit;"> παρατηρείται σε </span>αρνητικό δείκτη μεταυλικό<span style="vertical-align: inherit;"><span style="vertical-align: inherit;">.</span><span style="vertical-align: inherit;">Η </span></span>πίεση ακτινοβολίας<span style="vertical-align: inherit;"> στο </span>μεταυλικό<span style="vertical-align: inherit;"> είναι επίσης αρνητική </span><span style="vertical-align: inherit;"> επειδή η δύναμη ορίζεται ως:</span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">F=dp/dt</span></span><span style="font-family: verdana;"> </span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> Υπάρχει επίσης </span></span>αρνητική πίεση<span style="vertical-align: inherit;"> στη </span>σκοτεινή ενέργεια<span style="vertical-align: inherit;"><span style="vertical-align: inherit;">.</span><span style="vertical-align: inherit;">Χρησιμοποιώντας αυτές τις παραπάνω εξισώσεις,η σχέση </span></span>ενέργειας-ορμής<span style="vertical-align: inherit;"> πρέπει να είναι:</span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><span style="font-family: verdana; vertical-align: inherit;"><span style="font-family: verdana; vertical-align: inherit;">E</span><sup style="background-color: transparent; line-height: 19px;">2</sup>=-p</span></span></span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="background-color: transparent; font-family: verdana; vertical-align: inherit;">·c<sup style="background-color: transparent; line-height: 19px;">2</sup>+m<span style="font-size: x-small;">0</span></span><span style="background-color: transparent; font-family: verdana;"><sup style="line-height: 19px;">2</sup></span><span style="font-family: verdana;">·c</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">4</sup><span style="background-color: transparent; font-family: verdana;"> </span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"> Αντικατάσταση της </span>σχέσης Planck-Einstein:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">E=</span><span style="font-family: verdana;"><i style="text-align: left;">ħ</i></span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">ω</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">και της σχέσης </span>de Broglie:<span style="vertical-align: inherit;"> </span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><span style="font-family: verdana;">p=</span><span style="font-family: verdana;"><i style="text-align: left;">ħ</i></span></span></span><span style="font-family: verdana;">·</span><span style="font-family: verdana;">k</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><br /></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;">λαμβάνουμε την ακόλουθη </span><span style="font-family: verdana;">σχέση διασποράς:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><span style="font-family: verdana; vertical-align: inherit;"><span style="font-family: verdana; vertical-align: inherit;">ω</span><sup style="background-color: transparent; line-height: 19px;">2</sup>=-k</span></span></span><sup style="background-color: transparent; line-height: 19px;">2</sup><span style="background-color: transparent; font-family: verdana; vertical-align: inherit;">·c<sup style="background-color: transparent; line-height: 19px;">2</sup>+ω<span style="font-size: xx-small;">p</span></span><span style="background-color: transparent; font-family: verdana;"><sup style="line-height: 19px;">2</sup></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span class="mwe-math-element"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span class="mwe-math-element"><span style="font-family: verdana;">E<span style="font-size: x-small;">0</span>=</span><span style="font-family: verdana;"><i style="text-align: left;">ħ</i></span></span><span style="font-family: verdana;">·</span><span class="mwe-math-element"><span style="font-family: verdana;">ω=</span></span><span style="background-color: transparent; font-family: verdana; vertical-align: inherit;">-</span><span style="background-color: transparent; font-family: verdana;">m<span style="font-size: x-small;">0</span></span><span style="font-family: verdana;">·c<sup style="background-color: transparent; line-height: 19px;">2</sup>>0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">του κύματος αποτελείται από ένα ρεύμα σωματιδίων των οποίων η </span>ενέργεια-ορμή σχέση<span style="vertical-align: inherit;"> είναι:</span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="font-family: verdana; vertical-align: inherit;">E</span><sup style="background-color: transparent; line-height: 19px;">2</sup>=-p</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="background-color: transparent; font-family: verdana; vertical-align: inherit;">·c<sup style="background-color: transparent; line-height: 19px;">2</sup>+m<span style="font-size: x-small;">0</span></span><span style="background-color: transparent; font-family: verdana;"><sup style="line-height: 19px;">2</sup></span><span style="font-family: verdana;">·c</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">4</sup><span style="background-color: transparent; font-family: verdana;"> </span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><br /></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">το δυαδικό κύμα–σωματιδίων<span style="vertical-align: inherit;"> μπορεί να γραφτεί:</span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">υ=c</span></span><span style="font-family: verdana;">·</span><span style="font-family: verdana;"><span style="vertical-align: inherit;">(E<span style="font-size: xx-small;">0</span></span></span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana;">/</span><span style="font-family: verdana; vertical-align: inherit;">E</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana;"> - 1)</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">1/2</sup></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><br /></span></span></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">υ=c</span></span></span></span><span style="font-family: verdana;">·</span><span style="font-family: verdana;"><span style="vertical-align: inherit;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">(ω<span style="font-size: xx-small;">0</span></span></span><sup style="background-color: transparent; line-height: 19px;">2</sup>/<span style="font-family: verdana; vertical-align: inherit;">ω</span><sup style="background-color: transparent; line-height: 19px;">2</sup> - 1)</span></span><span style="font-family: verdana; font-size: 13.3333px;">1/2</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><br /></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;">και το εύρος είναι από μηδέν έως άπειρο:</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana; vertical-align: inherit;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">ω<span style="font-size: xx-small;">p</span></span></span><sup style="background-color: transparent; line-height: 19px;">2</sup>/<span style="font-family: verdana; vertical-align: inherit;">ω</span><sup style="background-color: transparent; line-height: 19px;">2</sup><2 </span><span class="mwe-math-element"><span style="font-family: verdana;">όταν </span></span><span style="font-family: verdana;">υ<c</span></p><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"><span style="font-family: verdana;"><span class="mwe-math-element"><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"></dl></span><span class="mwe-math-element"><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"><span class="mwe-math-element"><br /></span><span class="mwe-math-element"><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"><span class="mwe-math-element">και</span><span class="mwe-math-element"><dl style="background-color: white; color: #202122; margin-bottom: 0.5em; margin-top: 0.2em;"><span class="mwe-math-element"><br /></span></dl></span></dl></span></dl></span></span></dl><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span class="mwe-math-element"><span style="font-family: verdana;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">ω<span style="font-size: xx-small;">p</span></span></span><sup style="background-color: transparent; line-height: 19px;">2</sup>/<span style="font-family: verdana; vertical-align: inherit;">ω</span><sup style="background-color: transparent; line-height: 19px;">2</sup>>2 </span></span><span style="font-family: verdana;">για </span><span style="font-family: verdana;">υ>c</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span class="mwe-math-element"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"> Επιπλέον,η </span>κινητική ενέργεια<span style="vertical-align: inherit;"> <b>K</b> είναι επίσης αρνητική:</span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">K=E-E<span style="font-size: xx-small;">0</span></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">K=</span></span><span style="font-family: verdana; vertical-align: inherit;">-</span><span style="background-color: transparent; font-family: verdana;">m<sup style="line-height: 19px;">2</sup></span><span style="font-family: verdana;">·c</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana;"><span style="vertical-align: inherit;">-(</span></span><span style="background-color: transparent; font-family: verdana; vertical-align: inherit;">-</span><span style="background-color: transparent; font-family: verdana;">m<span style="font-size: xx-small;">0</span><sup style="line-height: 19px;">2</sup></span><span style="font-family: verdana;">·c<sup style="background-color: transparent; line-height: 19px;">2</sup> )</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">K</span><span style="font-family: verdana;">=-</span><span style="font-family: verdana;">m</span><span style="font-family: verdana; font-size: x-small;">0</span><span style="font-family: verdana;">·</span><span style="background-color: transparent; font-family: verdana;">c</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana; font-size: large;">/</span><span style="font-family: verdana;">(1+</span><span style="background-color: transparent; font-family: verdana;">υ</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana;">/</span><span style="background-color: transparent; font-family: verdana;">c</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="font-family: verdana;">)</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">1/2</sup><span style="font-family: verdana;"><span style="vertical-align: inherit;">+</span></span><span style="background-color: transparent; font-family: verdana;">m</span><span style="background-color: transparent; font-family: verdana; font-size: x-small;">0</span><span style="font-family: verdana;">·</span><span style="background-color: transparent; font-family: verdana;">c</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><br /></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;">K=</span></span><span style="background-color: transparent; font-family: verdana;">m</span><span style="font-family: verdana;"><span style="background-color: transparent; font-size: x-small;">0</span><span style="background-color: transparent;">·</span><span style="background-color: transparent;">c</span></span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="background-color: transparent; font-family: verdana;"><span style="font-size: x-large;">/</span>(1-1</span><span style="background-color: transparent; font-family: verdana; font-size: large;">/</span><span style="background-color: transparent; font-family: verdana;">(1+</span><span style="background-color: transparent; font-family: verdana;">υ</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="background-color: transparent; font-family: verdana;">/</span><span style="background-color: transparent; font-family: verdana;">c</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">2</sup><span style="background-color: transparent; font-family: verdana;">)</span><sup style="background-color: transparent; font-family: verdana; line-height: 19px;">1/2</sup><span style="font-family: verdana;"><0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;">m</span><span style="font-family: verdana; font-size: xx-small;">0</span><span style="font-family: verdana;"><0</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span class="mwe-math-element"><br /></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"> Στην πραγματικότητα,η </span>αρνητική κινητική ενέργεια<span style="vertical-align: inherit;"> υπάρχει σε ορισμένα μοντέλα</span><span style="vertical-align: inherit;"> για να περιγράψει τη </span>σκοτεινή ενέργεια<span style="vertical-align: inherit;"> (</span><span style="vertical-align: inherit;">φανταστική ενέργεια</span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">) των οποίων η πίεση είναι αρνητική.</span><span style="vertical-align: inherit;">Με αυτόν τον τρόπο,η </span></span>αρνητική μάζα<span style="vertical-align: inherit;"> της εξωτικής ύλης συνδέεται τώρα με την </span>αρνητική ορμή<span style="vertical-align: inherit;">,την </span>αρνητική πίεση<span style="vertical-align: inherit;">,την αρνητική κινητική ενέργεια και το <b>FTL</b> ( </span>γρηγορότερο από το φως<span style="vertical-align: inherit;">).</span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><b style="color: red; font-family: "Times New Roman"; white-space: nowrap;"><span style="font-family: verdana;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΣΤΗΝ ΘΕΩΡΙΑ ΤΩΝ ΔΥΝΑΜΙΚΩΝ ΣΥΣΤΗΜΑΤΩΝ</span></b></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> Στην </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">ομαδική θεωρητική</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> προσέγγιση της </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">ανάλυσης δυναμικών συστημάτων</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">,ο χειριστής αντιστροφής χρόνου είναι </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">πραγματικός</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> και η αντιστροφή χρόνου παράγει </span></span>αναστροφή ενέργεια και μάζα.<span style="vertical-align: inherit;"><span style="vertical-align: inherit;">Το <b>1970</b>,</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">ο J<b>ean-Marie Souriau</b></span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> απέδειξε,χρησιμοποιώντας την</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">μέθοδο τροχιάς </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">της πλήρους δυναμικής </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">ομάδας <b>Πουανκαρέ</b></span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">,δηλαδή η </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">δράση της ομάδας</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> για το </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">διπλό χώρο</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> της </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"><b>Lie άλγεβρα</b></span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">,ότι η αντιστροφή του </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">βέλους του χρόνου</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> ισούται με την αντιστροφή της ενέργειας ενός σωματιδίουκαι η μάζα του,εάν το σωματίδιο είναι ένα.</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">Στη </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"><b>γενική θεωρία της σχετικότητας</b></span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">,το σύμπαν περιγράφεται ως</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> πολλαπλό που</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> σχετίζεται με μια </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">μετρική τάση</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> λύση των εξισώσεων πεδίου του Αϊνστάιν.</span><span style="vertical-align: inherit;">Σε ένα τέτοιο πλαίσιο,η κινούμενη κίνηση απαγορεύει την ύπαρξη αρνητικής ύλης.</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">Μερικές </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">διμετρικές θεωρίες</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> του σύμπαντος προτείνουν ότι δύο </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">παράλληλα σύμπαντα</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> με ένα αντίθετο βέλος του χρόνου μπορεί να υπάρχουν αντί ενός,που συνδέονται μεταξύ τους από τη </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"><b>Μεγάλη Έκρηξη</b></span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> και αλληλεπιδρούν μόνο μέσω της </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">βαρύτητας</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">.</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">Το σύμπαν στη συνέχεια περιγράφεται ως πολλαπλό που σχετίζεται με δύο μετρήσεις,μία με θετική μάζα και η άλλη με αρνητική μάζα.</span><span style="vertical-align: inherit;">Σύμφωνα με τη θεωρία της ομάδας,το θέμα της </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">συζευγμένης</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> μέτρησης φαίνεται στην ύλη της άλλης μέτρησης να έχει αντίθετη μάζα και βέλος του χρόνου,αν και ο </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">κατάλληλος χρόνος του</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> θα παραμείνει θετικός.</span><span style="vertical-align: inherit;">Οι συζευγμένες μετρήσεις έχουν τη δική τους </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">γεωδαιστική </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">και είναι λύσεις δύο συζευγμένων εξισώσεων πεδίου.</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">Η αρνητική ύλη του συζευγμένου μετρικού,που αλληλεπιδρά με την ύλη της άλλης μέτρησης μέσω της βαρύτητας,θα μπορούσε να είναι μια εναλλακτική υποψήφια εξήγηση της </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">σκοτεινής ύλης</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">,της </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">σκοτεινής ενέργειας</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">,του </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">κοσμικού πληθωρισμού</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;"> και ενός </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">επιταχυνόμενου σύμπαντος</span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">.</span></span></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><b style="color: red; font-family: "Times New Roman"; white-space: nowrap;"><span style="font-family: verdana;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΣΤΟ ΝΟΜΟ ΤΗΣ ΒΑΡΥΤΗΤΑΣ ΤΟΥ GAUSS</span></b></span></span></p><p style="background-color: white; margin: 0.5em 0px; text-align: justify;"><span><span style="color: #202122; font-family: verdana; vertical-align: inherit;"> Στον ηλεκτρομαγνητισμό,μπορεί κανείς να αντλήσει την ενεργειακή πυκνότητα ενός πεδίου από το <b>νόμο του Gauss</b>,υποθέτοντας ότι η καμπύλη του πεδίου είναι <b>0</b>.Η εκτέλεση του ίδιου υπολογισμού χρησιμοποιώντας το <b>νόμο Gauss</b> για τη βαρύτητα παράγει μια αρνητική ενεργειακή πυκνότητα για ένα βαρυτικό πεδίο.</span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><b style="color: red; font-family: "Times New Roman"; white-space: nowrap;"><span style="font-family: verdana;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΣΤΗΝ ΒΑΡΥΤΙΚΗ ΑΛΛΙΛΕΠΙΔΡΑΣΗ ΤΗΣ ΑΝΤΙΥΛΗΣ</span></b></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Η συντριπτική πλειοψηφία των φυσικών πιστεύει ότι η αντιύλη έχει θετική μάζα και πρέπει να επηρεάζεται από τη βαρύτητα όπως και η φυσιολογική ύλη.Τα άμεσα πειράματα για το ουδέτερο αντιυδρογόνο δεν ήταν αρκετά ευαίσθητα για να ανιχνεύσουν οποιαδήποτε διαφορά μεταξύ της βαρυτικής αλληλεπίδρασης της αντιύλης,σε σύγκριση με την κανονική ύλη.</span><span style="font-family: verdana;">Τα πειράματα θαλάμου φυσαλίδων παρέχουν περαιτέρω ενδείξεις ότι τα αντισωματίδια έχουν την ίδια αδρανειακή μάζα με τα κανονικά αντίστοιχα.Σε αυτά τα πειράματα,ο θάλαμος υπόκειται σε ένα σταθερό μαγνητικό πεδίο που αναγκάζει τα φορτισμένα σωματίδια να ταξιδεύουν σε ελικοειδή διαδρομές,η ακτίνα και η κατεύθυνση των οποίων αντιστοιχούν στην αναλογία ηλεκτρικού φορτίου προς την αδρανειακή μάζα.Τα ζεύγη σωματιδίων–αντισωματιδίων φαίνεται να ταξιδεύουν σε έλικες με αντίθετες κατευθύνσεις αλλά ίδιες ακτίνες,υπονοώντας ότι οι λόγοι διαφέρουν μόνο σε σημείο.Αλλά αυτό δεν δείχνει αν είναι το φορτίο ή η αδρανειακή μάζα που αντιστρέφεται. Ωστόσο,παρατηρούνται ζεύγη σωματιδίων-αντισωματιδίων που έλκουν ηλεκτρικά το ένα το άλλο.Αυτή η συμπεριφορά υπονοεί ότι και οι δύο έχουν θετική αδρανειακή μάζα και αντίθετα φορτία.Αν το αντίστροφο ήταν αληθές,τότε το σωματίδιο με θετική αδρανειακή μάζα θα απωθούσε από τον αντισωματικό εταίρο του.</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"><span style="vertical-align: inherit;"><b style="color: red; font-family: "Times New Roman"; white-space: nowrap;"><span style="font-family: verdana;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΣΤΗΝ ΚΒΑΝΤΙΚΗ ΜΗΧΑΝΙΚΗ</span></b></span></span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Το <b>1928</b>,η <b>θεωρία του Paul Dirac</b> για τα στοιχειώδη σωματίδια,τώρα μέρος του <b>Πρότυπου μοντέλου(Standard Model)</b>,περιλάμβανε ήδη αρνητικές λύσεις.Το πρότυπο μοντέλο είναι μια γενίκευση της <b>κβαντικής ηλεκτροδυναμικής (QED)</b> και η αρνητική μάζα έχει ήδη ενσωματωθεί στη θεωρία.</span><span style="font-family: verdana;">Οι </span><b style="font-family: verdana;">Morris,Thorne</b><span style="font-family: verdana;"> και </span><b style="font-family: verdana;">Yurtsever</b><span style="font-family: verdana;"> επεσήμαναν ότι η κβαντική μηχανική του </span><b style="font-family: verdana;">φαινομένου Casimir</b><span style="font-family: verdana;"> μπορεί να χρησιμοποιηθεί για την παραγωγή μίας τοπικά αρνητικής μάζας περιοχής χωροχρόνου. Σε αυτό το άρθρο, και σε επακόλουθη εργασία άλλων,έδειξαν ότι η αρνητική ύλη θα μπορούσε να χρησιμοποιηθεί για τη σταθεροποίηση μιας σκουληκότρυπας.Ο </span><b style="font-family: verdana;">Cramer</b><span style="font-family: verdana;"> υποστηρίζει ότι τέτοιες σκουληκότρυπες μπορεί να έχουν δημιουργηθεί στον πρώιμο κόσμο,σταθεροποιημένες από βρόχους αρνητικής μάζας κοσμικής χορδής.Ο </span><b style="font-family: verdana;">Stephen Hawking</b><span style="font-family: verdana;"> υποστήριξε ότι η αρνητική ενέργεια είναι απαραίτητη προϋπόθεση για τη δημιουργία μιας κλειστής χρονικής καμπύλης με χειραγώγηση των βαρυτικών πεδίων σε μια πεπερασμένη περιοχή του διαστήματος.Αυτό σημαίνει,για παράδειγμα,ότι ένας πεπερασμένος </span><b style="font-family: verdana;">κύλινδρος Tipler </b><span style="font-family: verdana;">δεν μπορεί να χρησιμοποιηθεί ως μηχανή χρόνου.</span></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><b style="color: red; white-space: nowrap;"><span style="font-family: verdana;">ΑΡΝΗΤΙΚΗ ΜΑΖΑ ΣΤΗΝ </span></b><b style="color: red; font-family: verdana; text-align: left; white-space: nowrap;">ΕΞΙΣΩΣΗ SCHRÖDINGER</b></p><p style="background-color: white; color: #202122; margin: 0.5em 0px; text-align: justify;"><span style="font-family: verdana;"> Για ενεργειακά ιδιοσυστήματα της <b>εξίσωσης Schrödinger</b>,η κυματοσύνδεση είναι κυματοειδής όπου η ενέργεια του σωματιδίου είναι μεγαλύτερη από το τοπικό δυναμικό,και εκθετική όπου είναι μικρότερη.Αυτό θα σήμαινε ότι η κινητική ενέργεια είναι αρνητική στις εξερχόμενες περιοχές για να ακυρώσει το τοπικό δυναμικό.Ωστόσο,η κινητική ενέργεια είναι ένας χειριστής της κβαντικής μηχανικής και η τιμή προσδοκίας της είναι πάντα θετική,αθροίζοντας με την προσδοκώμενη τιμή της δυνητικής ενέργειας για να αποδώσει την ενεργειακή ιδιοτιμή.</span><span style="font-family: verdana;">Για κυματοσυσκευές σωματιδίων με μάζα μηδενικής ανάπαυσης,όπως φωτόνια,σημαίνει ότι τυχόν εξερχόμενα τμήματα της κυματοσύνδεσης θα σχετίζονται με μια τοπική αρνητική μάζα-ενέργεια.Ωστόσο,η </span><b style="font-family: verdana;">εξίσωση Schrödinger</b><span style="font-family: verdana;"> δεν ισχύει για σωματίδια χωρίς μάζα.Αντ 'αυτού απαιτείται η </span><b style="font-family: verdana;">εξίσωση Klein–Gordon</b><span style="font-family: verdana;">.</span></p><p></p><p style="text-align: justify;"><span style="color: red; font-family: verdana; text-align: center;"><b>ΧΡΗΣΗ ΤΗΣ ΑΡΝΗΤΙΚΗΣ ΜΑΖΑΣ ΓΙΑ ΔΙΑΣΤΡΙΚΑ ΤΑΞΙΔΙΑ<br /></b></span></p><p style="text-align: justify;"><span style="font-family: verdana;"><span style="text-align: center;"> Η χρήση των ιδιοτήτων της αρνητικής μάζας (αν υπάρχει) για διαστρικά ταξίδια εξάπτει την φαντασία των επιστημόνων.Ένα διαστημόπλοιο το οποίο θα μπορεί να εφαρμόσει να</span><span style="text-align: center;"> χρησιμοποιεί θετική και αρνητική μάζα για να επιταχύνει συνεχώς.</span></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnYwBk4OiIfvr9akKRN5laWPMWHlDdW6MTDE5BdWCK1u4f-2bvG0IjcAj_NthyHCrR-w1X4xnMVt_BBz_Tbm7mooDfaCatpeaYvCWxvJVYXp9wVO_LZlx2sfIB3zC0-N7RlKiI3XO56g0/s728/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259114.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="410" data-original-width="728" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnYwBk4OiIfvr9akKRN5laWPMWHlDdW6MTDE5BdWCK1u4f-2bvG0IjcAj_NthyHCrR-w1X4xnMVt_BBz_Tbm7mooDfaCatpeaYvCWxvJVYXp9wVO_LZlx2sfIB3zC0-N7RlKiI3XO56g0/w640-h360/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259114.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><span style="color: #800180; font-family: verdana;"><span>Ένα διαστημόπλοιο το οποίο θα μπορεί να εφαρμόσει να</span><span> χρησιμοποιεί θετική και αρνητική μάζα για να επιταχύνει συνεχώς</span></span></b></td></tr></tbody></table><p></p><p style="text-align: justify;"><span style="font-family: verdana;"><span style="text-align: center;"> Ο <b>Banesh Hoffman</b> απέδειξε πως ένα σώμα μπορεί να μεταβάλει την μάζα του από θετική σε αρνητική και από αρνητική σε θετική αν εκπέμψει ποσά ενέργειας με την μορφή βαρυτικών κυμάτων.Έτσι το διαστημόπλοιο θα μπορεί να αυξήσει την ταχύτητα του.</span><span style="text-align: center;">Ωστόσο το διαστημόπλοιο δεν μπορεί να φτάσει ή ακόμα και να ξεπεράσει την ταχύτητα του φωτός,σύμφωνα με τον <b>Άλμπερτ Αϊνστάιν</b>.</span></span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJe6Ars1ELJqhQ1Fml5CODXizCnj_WwNm-BeeAL1gmYQNoMhJVQ2Sc5VaSPM5SB7-a5gjKkVX9GUf6_uxfDdSv4MZmWHP1h9P-YarGEk0_tNR4auFwB9nZGiO3VQVi9417qLWgkOtEuw8/s1620/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259118.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="791" data-original-width="1620" height="312" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJe6Ars1ELJqhQ1Fml5CODXizCnj_WwNm-BeeAL1gmYQNoMhJVQ2Sc5VaSPM5SB7-a5gjKkVX9GUf6_uxfDdSv4MZmWHP1h9P-YarGEk0_tNR4auFwB9nZGiO3VQVi9417qLWgkOtEuw8/w640-h312/%25CE%2591%25CE%25A1%25CE%259D%25CE%2597%25CE%25A4%25CE%2599%25CE%259A%25CE%2589+%25CE%259C%25CE%2591%25CE%2596%25CE%259118.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white;"><span style="color: #800180; font-family: verdana;"><b>Η αρνητική ύλη μπορεί να βοηθήσει στον χειρισμό του χωροχρόνου,επιτρέποντας σε μια κίνηση στημονιού να ταξιδεύει με πολύ μεγάλες ταχύτητες</b></span></span></td></tr></tbody></table><p></p><p style="text-align: justify;"><span style="font-family: verdana;"><span style="text-align: center;"> Όμως το <b>1994 </b>ο <b>Μεξικανός</b> φυσικός <b>Miguel Alcubierre</b> βασισμένος στους υπολογισμούς του <b>Αϊνστάιν</b> ανακοίνωσε πως ένα διαστημόπλοιο περιτριγυρισμένο από φυσαλίδα αρνητικής μάζας μπορεί να χρησιμοποιήσει τον χωρόχρονο για να πραγματοποιήσει ταξίδια που ξεπερνάνε την ταχύτητα του φωτός.</span></span></p><p style="text-align: justify;"><b><span style="color: red; font-family: verdana;">ΒΙΒΛΙΟΓΡΑΦΙΑ</span></b></p><p style="text-align: justify;"><span style="font-family: verdana;"><b>1.</b> https://en.wikipedia.org/wiki/Negative_mass</span></p><p style="text-align: justify;"><span style="font-family: verdana;"><b>2.</b> https://el.wikipedia.org/wiki/</span><span style="text-align: left;"><span style="font-family: verdana;">Αρνητική_μάζα</span></span></p><p style="text-align: justify;"><span style="text-align: left;"><span style="font-family: verdana;"><b>3.</b> https://physicsgg.me/2017/04/20/</span></span><span style="text-align: left;"><span style="font-family: verdana;">η-αρνητική-μάζα-θα-ήταν-πολύ-διασκεδασ/</span></span></p><p style="text-align: justify;"><span style="text-align: left;"><span style="font-family: verdana;"><b>4. </b>https://testtubegames.com/blog/negative-mass/</span></span></p></div>ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.com0tag:blogger.com,1999:blog-6644102595821010388.post-88457734595702928812020-11-25T14:15:00.000-08:002020-11-27T14:17:28.310-08:00ΣΚΟΤΕΙΝΟ ΥΓΡΟ<p style="text-align: justify;"><span style="text-align: left;"><span style="color: red; font-family: verdana; font-size: x-large;"><b>ΣΚΟΤΕΙΝΟ ΥΓΡΟ</b></span></span></p><p style="text-align: justify;"><span style="color: red; font-family: verdana;"></span></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: justify;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdZK6Kz8O3gPOPZkypCm5KvHEJnmS36l1h0BdO7se3siwkYjOaHJCIVNyJn3Ge0cvpUJpRz6Hdb_VDV5TgaAM-iNFxDerDsjfaNOhqH7jPShzzbPydXESvAHltYRC3pdv3oMCd_4Lxoqw/s400/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F7.jpg" style="margin-left: auto; margin-right: auto;"><span style="font-family: verdana;"><img border="0" data-original-height="400" data-original-width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdZK6Kz8O3gPOPZkypCm5KvHEJnmS36l1h0BdO7se3siwkYjOaHJCIVNyJn3Ge0cvpUJpRz6Hdb_VDV5TgaAM-iNFxDerDsjfaNOhqH7jPShzzbPydXESvAHltYRC3pdv3oMCd_4Lxoqw/s16000/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F7.jpg" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="color: #800180; font-family: verdana; font-size: large;"><b>ΣΚΟΤΕΙΝΟ ΥΓΡΟ</b></span></td></tr></tbody></table><p></p><p style="text-align: justify;"><span style="color: red; font-family: verdana;"><b>ΕΙΣΑΓΩΓΗ</b></span></p><p style="text-align: justify;"><span style="font-family: verdana;"> <b><span style="color: #2b00fe;">Σκοτεινό υγρό</span>,στην αστρονομία και την κοσμολογία ονομάζεται μία εναλλακτική θεωρία για τη σκοτεινή ύλη και τη σκοτεινή ενέργεια που επιχειρεί να εξηγήσει και τα δύο φαινόμενα σε ένα ενιαίο πλαίσιο.</b></span></p><p style="text-align: justify;"><span style="font-family: verdana;"></span></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: justify;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfp_T1gUHo2laddxl4J2vaBvqx5Qd2DP3_tvd_y_1QbW0WXZTmECNKZhUGm0dqHWKlNXQjx1myfh23ueS20RDCnU68GDSlj2kCI7LfRokHHziUlZ9XV6VQhvAbVf4ladcGEVRZ_0xV6BU/s696/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F4.jpg" style="margin-left: auto; margin-right: auto;"><span style="font-family: verdana;"><img border="0" data-original-height="450" data-original-width="696" height="414" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfp_T1gUHo2laddxl4J2vaBvqx5Qd2DP3_tvd_y_1QbW0WXZTmECNKZhUGm0dqHWKlNXQjx1myfh23ueS20RDCnU68GDSlj2kCI7LfRokHHziUlZ9XV6VQhvAbVf4ladcGEVRZ_0xV6BU/w640-h414/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F4.jpg" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b style="text-align: justify;"><span style="color: #800180; font-family: verdana;">Σκοτεινό υγρό,στην αστρονομία και την κοσμολογία ονομάζεται μία εναλλακτική θεωρία για τη σκοτεινή ύλη και τη σκοτεινή ενέργεια που επιχειρεί να εξηγήσει και τα δύο φαινόμενα σε ένα ενιαίο πλαίσιο</span></b></td></tr></tbody></table><p></p><div style="text-align: justify;"><span style="font-family: verdana;"><span style="font-family: verdana;"> Το σκοτεινό υγρό προτείνει ότι η σκοτεινή ύλη και η σκοτεινή ενέργεια δεν είναι ξεχωριστά φυσικά φαινόμενα όπως θεωρούνται </span><span style="background-color: white; color: #202122; text-align: start;"><span style="font-family: verdana;">γενικά</span></span><span style="font-family: verdana;">,ούτε έχουν ξεχωριστές προελεύσεις,αλλά ότι συνδέονται μεταξύ τους και μπορούν να θεωρηθούν ως δύο όψεις ενός μεμονωμένου υγρού και έχουν παραχθεί ως υποπροϊόντα νέων προτεινόμενων εκτεταμένων νόμων της βαρύτητας σε πολύ μεγάλες κλίμακες.Οι </span>εναλλακτικές θεωρίες της εκτεταμένης βαρύτητας,όπως η τροποποιημένη νευτώνεια δυναμική <b>(MOND)</b>,τις παρουσιάζει ως συγκεκριμένα υποπροϊόντα.</span></div><p></p><p style="text-align: justify;"></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: justify;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTtPoLaIXNYER8MjcyjQK9TZOEwwVYknhZViKHwhIcRxmc9MqkjrGgzPudh-YSsqCmFPz5654bSmy4XZuqSJY8iYPW9UD5s-GB2Cq-JN_4M3ugfmRCPQuDWLCi5vVvuFKk1w732i-0nbs/s512/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F3.jpg" style="margin-left: auto; margin-right: auto;"><span style="font-family: verdana;"><img border="0" data-original-height="348" data-original-width="512" height="436" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTtPoLaIXNYER8MjcyjQK9TZOEwwVYknhZViKHwhIcRxmc9MqkjrGgzPudh-YSsqCmFPz5654bSmy4XZuqSJY8iYPW9UD5s-GB2Cq-JN_4M3ugfmRCPQuDWLCi5vVvuFKk1w732i-0nbs/w640-h436/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F3.jpg" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-family: verdana; text-align: justify;"><span style="color: #800180;"><b>Στις γαλαξιακές κλίμακες,το σκοτεινό υγρό συμπεριφέρεται σαν σκοτεινή ύλη και σε μεγαλύτερες κλίμακες η συμεριφορά του γίνεται παρόμοια με τη σκοτεινή ενέργεια</b></span></span></td></tr></tbody></table><span style="font-family: verdana;"></span><p></p><div style="text-align: justify;"><span style="font-family: verdana;"> Στις γαλαξιακές κλίμακες,το σκοτεινό υγρό συμπεριφέρεται σαν σκοτεινή ύλη και σε μεγαλύτερες κλίμακες η συμεριφορά του γίνεται παρόμοια με τη σκοτεινή ενέργεια.Οι παρατηρήσεις των νόμων της βαρύτητας που προσομοιώνονται από παρατηρήσεις στη γήινη κλίμακα και την κλίμακα του <b>Ηλιακού Συστήματος</b>,θεωρούνται ανεπαρκείς να εξηγήσουν τα βαρυτικά αποτελέσματα σε αυτές τις μεγαλύτερες κλίμακες.Ένα απλό σκοτεινό υγρό με αρνητική μάζα που προτάθηκε το <b>2018</b> από τον αστροφυσικό<b> Jamie Farnes </b>από το <b>Πανεπιστήμιο της Οξφόρδης </b>έχει αποδειχθεί ότι έχει τις ιδιότητες που απαιτούνται για να εξηγήσει τόσο τη σκοτεινή ύλη όσο και τη σκοτεινή ενέργεια.</span></div><p></p><p style="text-align: justify;"><span style="color: red; font-family: verdana;"><b>ΕΠΙΣΚΟΠΗΣΗ ΜΕΛΕΤΗΣ ΣΚΟΤΕΙΝΟΥ ΥΓΡΟΥ</b></span></p><p style="text-align: justify;"><span style="font-family: verdana;"> Τ</span><span style="font-family: verdana;">α τελευταία χρόνια,δ</span><span style="font-family: verdana;">ύο μεγάλα αινίγματα έχουν προκύψει στην αστροφυσική και στην κοσμολογία που ασχολούνται με τους νόμους της βαρύτητας.Το πρώτο ήταν η συνειδητοποίηση ότι δεν υπάρχουν αρκετά ορατά αστέρια ή αέριο μέσα στους γαλαξίες για να εξηγήσουν τον υψηλό ρυθμό περιστροφής τους.Η υπόθεση της σκοτεινής ύλης δημιουργήθηκε για να εξηγήσει αυτό το φαινόμενο.Υποδηλώνει ότι οι γαλαξίες (συμπεριλαμβανομένου του δικού μας <b>Γαλαξία</b>) περιστρέφονται τόσο γρήγορα όσο υπάρχει περισσότερη ύλη σε αυτούς τους γαλαξίες από ότι μπορεί να φανεί με το άθροισμα μόνο της μάζας των αστεριών και του αερίου και ότι αυτή η αόρατη (σκοτεινή) ύλη είναι αόρατη επειδή δεν αλληλεπιδρά με την ηλεκτρομαγνητική δύναμη από την οποία προέρχονται όλες οι μορφές του φωτός.</span></p><p style="text-align: justify;"></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: justify;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjA7ovS8elhLkt_HdAkP07rPZ6LpaXXOv8fMogVmUn1sfgD49-xu2y1o1-E_LX75LkaoBJkz6FL-VLD-_AzTR6DK50Lf7c4otct83FVg3w1KhZn0VTgJGQnhxpkpHnvvD9PFj5Fx5fWH9c/s1024/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F2.jpg" style="margin-left: auto; margin-right: auto;"><span style="font-family: verdana;"><img border="0" data-original-height="415" data-original-width="1024" height="260" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjA7ovS8elhLkt_HdAkP07rPZ6LpaXXOv8fMogVmUn1sfgD49-xu2y1o1-E_LX75LkaoBJkz6FL-VLD-_AzTR6DK50Lf7c4otct83FVg3w1KhZn0VTgJGQnhxpkpHnvvD9PFj5Fx5fWH9c/w640-h260/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F2.jpg" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-family: verdana; text-align: justify;"><b><span style="color: #800180;">Ένα απλό σκοτεινό υγρό με αρνητική μάζα</span></b></span></td></tr></tbody></table><span style="font-family: verdana;"></span><p></p><div style="text-align: justify;"><span style="font-family: verdana;"> Η υποθετική σκοτεινή ύλη επεκτάθηκε στη συνέχεια σε συστάδες γαλαξιών και βρέθηκε χρήσιμη για κοσμολογικούς υπολογισμούς και για την ερμηνεία του βαρυτικού φακού από τους γαλαξίες.Το δεύτερο αίνιγμα προήλθε από τις παρατηρήσεις ενός πολύ συγκεκριμένου είδους σουπερνόβα,γνωστού ως <b>σουπερνόβα τύπου Ia</b>.Όταν συγκρίθηκαν σε απομακρυσμένους και κοντινούς γαλαξίες,διαπιστώθηκε ότι το μακρινό σουπερνόβα ήταν πιο αχνό από το αναμενόμενο,και έτσι πιο μακριά από το αναμενόμενο.Αυτό σήμαινε ότι το <b>Σύμπαν </b>όχι μόνο επεκτείνεται,αλλά επιταχύνει την επέκτασή του.Η υποθετική σκοτεινή ενέργεια μπορεί να εξηγήσει αυτό το φαινόμενο.Η παραδοσιακή προσέγγιση στη μοντελοποίηση των επιπτώσεων της βαρύτητας προϋποθέτει ότι η γενική σχετικότητα είναι εξίσου έγκυρη σε κοσμολογικές κλίμακες όπως και στο <b>Ηλιακό Σύστημα</b>,όπου οι προβλέψεις του έχουν δοκιμαστεί με μεγαλύτερη ακρίβεια.Ωστόσο,η μη αλλαγή των κανόνων της βαρύτητας συνεπάγεται την παρουσία σκοτεινής ύλης και σκοτεινής ενέργειας σε μέρη του <b>Σύμπαντος </b>όπου η καμπυλότητα του πολλαπλού χωροχρόνου είναι πολύ μικρότερη από αυτήν στο <b>Ηλιακό Σύστημα</b>.</span></div><span style="font-family: verdana;"><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: justify;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQRX1maG1U_VGMMwqTzUShe0d4DLTUClfVhfZ0tQvJxh_eBvlJkOn1oRkC8Lkrp2rPsSo5BUBIOXsYfSi39jrKZOrMwBIPCFiktUkJlLoYP642TO0cfLRiKpmrXlB7jhpHDLEZCM2D2kw/s1920/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F6.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1080" data-original-width="1920" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQRX1maG1U_VGMMwqTzUShe0d4DLTUClfVhfZ0tQvJxh_eBvlJkOn1oRkC8Lkrp2rPsSo5BUBIOXsYfSi39jrKZOrMwBIPCFiktUkJlLoYP642TO0cfLRiKpmrXlB7jhpHDLEZCM2D2kw/w640-h360/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F6.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="text-align: justify;"><span style="color: #800180;"><b>Η θεωρία του σκοτεινού υγρού υποθέτει ότι το σκοτεινό υγρό είναι ένα συγκεκριμένο είδος υγρού του οποίου οι ελκυστικές και απωθητικές συμπεριφορές εξαρτώνται από την τοπική ενεργειακή πυκνότητα</b></span></span></td></tr></tbody></table></span><p></p><p style="text-align: justify;"></p><div style="text-align: justify;"><span style="font-family: verdana;"> Είναι φαινομενολογικά δυνατό να μεταβληθούν οι εξισώσεις της βαρύτητας σε περιοχές με χαμηλή καμπυλότητα χωροχρόνου έτσι ώστε η δυναμική του χωροχρόνου να προκαλεί αυτό που αποδίδουμε στην παρουσία της σκοτεινής ύλης και της σκοτεινής ενέργειας.</span><span style="font-family: verdana;">Η θεωρία του σκοτεινού υγρού υποθέτει ότι το σκοτεινό υγρό είναι ένα συγκεκριμένο είδος υγρού του οποίου οι ελκυστικές και απωθητικές συμπεριφορές εξαρτώνται από την τοπική ενεργειακή πυκνότητα.Σε αυτή τη θεωρία,το σκοτεινό υγρό συμπεριφέρεται σαν σκοτεινή ύλη στις περιοχές του διαστήματος όπου η πυκνότητα του βαρυονίου είναι υψηλή.Η ιδέα είναι ότι όταν το σκοτεινό υγρό είναι παρουσία ύλης,επιβραδύνεται και πήζει γύρω από αυτό.Αυτό στη συνέχεια προσελκύει περισσότερο σκοτεινό υγρό για να πήζει γύρω από αυτό,ενισχύοντας έτσι τη δύναμη της βαρύτητας κοντά σε αυτό.Το αποτέλεσμα είναι πάντα παρόν,αλλά γίνεται αισθητό μόνο με την παρουσία μιας πολύ μεγάλης μάζας, όπως ένας γαλαξίας.Αυτή η περιγραφή είναι παρόμοια με τις θεωρίες της σκοτεινής ύλης και μια ειδική περίπτωση των εξισώσεων του σκοτεινού υγρού αναπαράγει τη σκοτεινή ύλη.</span></div><span style="font-family: verdana;"><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: justify;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxGt5ecAWG7Pn-wCpcXtTxy04mSw815SCvVNqUzqGzk8OlFJPDFktT6zG76Zuzm5QYIVRMcYfzEOez-eltWo7oWkUx9S_mA7VwNLtnZG751KnO0TIM9eQGrDnGLIlUw2rZldptTl03_2k/s715/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F5.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="402" data-original-width="715" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxGt5ecAWG7Pn-wCpcXtTxy04mSw815SCvVNqUzqGzk8OlFJPDFktT6zG76Zuzm5QYIVRMcYfzEOez-eltWo7oWkUx9S_mA7VwNLtnZG751KnO0TIM9eQGrDnGLIlUw2rZldptTl03_2k/w640-h360/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F5.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="text-align: justify;"><span style="color: #800180;"><b>Η ιδέα είναι ότι όταν το σκοτεινό υγρό είναι παρουσία ύλης,επιβραδύνεται και πήζει γύρω από αυτό</b></span></span></td></tr></tbody></table></span><span style="font-family: verdana;"><div style="text-align: justify;"> Από την άλλη πλευρά,σε μέρη όπου υπάρχει σχετικά μικρή ύλη,όπως στα κενά μεταξύ γαλαξιακών υπερκαυστήρων,αυτή η υπόθεση προβλέπει ότι το σκοτεινό υγρό χαλαρώνει και αποκτά αρνητική πίεση.Έτσι το σκοτεινό υγρό γίνεται μια απωθητική δύναμη,με αποτέλεσμα παρόμοιο με αυτό της σκοτεινής ενέργειας.Το σκοτεινό υγρό υπερβαίνει τη σκοτεινή ύλη και τη σκοτεινή ενέργεια,καθώς προβλέπει ένα συνεχές φάσμα ελκυστικών και αποκρουστικών ιδιοτήτων σε διάφορες περιπτώσεις πυκνότητας ύλης.Πράγματι,ειδικές περιπτώσεις διαφόρων άλλων βαρυτικών θεωριών αναπαράγονται από το σκοτεινό υγρό,όπως ο <b>πληθωρισμός</b>,η <b>πεμπτουσία</b>,η <b>k-ουσία</b>,η <b>f (R)</b>,η <b>Generalized Einstein-Aether f (K)</b>,η <b>MOND</b>,η <b>TeVeS</b>,η <b>BSTV</b> κ.λπ. προτείνει νέα μοντέλα,όπως ένα συγκεκριμένο μοντέλο <b>f(K+R) </b>που προτείνει ενδιαφέρουσες διορθώσεις στο<b> MOND</b> που εξαρτώνται από την κόκκινη μετατόπιση και την πυκνότητα.</div></span><p></p><p style="text-align: justify;"><span style="font-family: verdana;"><b><span style="color: red;">ΑΠΛΟΠΟΙΗΣΗ ΠΑΡΑΔΟΧΩΝ</span></b></span></p><p style="text-align: justify;"><span style="font-family: verdana;"><span style="color: red;"><b> </b></span>Το σκοτεινό ρευστό δεν αναλύεται όπως ένα τυπικό μοντέλο μηχανικής ρευστού,επειδή οι πλήρεις εξισώσεις στη μηχανική των ρευστών είναι ακόμη πολύ δύσκολο να επιλυθούν.</span></p><p style="text-align: justify;"></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: justify;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSQ9yitdLuZwS1VUUNr5_Ng10Z7Wtuy24Cc8jzSMFl2UYqwLHRG2h4CzlIThsD1qNj_8VBOpOeo6UzAGxCkA8mMhr93W5envTSYdE5GJffAv7he4hPrSU1It9ufYT9DXen3-d8JQqYfq0/s496/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F1.jpg" style="margin-left: auto; margin-right: auto;"><span style="font-family: verdana;"><img border="0" data-original-height="331" data-original-width="496" height="429" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSQ9yitdLuZwS1VUUNr5_Ng10Z7Wtuy24Cc8jzSMFl2UYqwLHRG2h4CzlIThsD1qNj_8VBOpOeo6UzAGxCkA8mMhr93W5envTSYdE5GJffAv7he4hPrSU1It9ufYT9DXen3-d8JQqYfq0/w640-h429/%25CE%25A3%25CE%259A%25CE%259F%25CE%25A4%25CE%2595%25CE%2599%25CE%259D%25CE%259F+%25CE%25A5%25CE%2593%25CE%25A1%25CE%259F1.jpg" width="640" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-family: verdana; text-align: justify;"><span style="color: #800180;"><b>Το σκοτεινό ρευστό δεν αναλύεται όπως ένα τυπικό μοντέλο μηχανικής ρευστού</b></span></span></td></tr></tbody></table><span style="font-family: verdana;"></span><p></p><div style="text-align: justify;"><span style="font-family: verdana;"> Μια τυποποιημένη μηχανική προσέγγιση ρευστού,όπως το γενικευμένο μοντέλο <b>αερίου Chaplygin</b>,θα ήταν μια ιδανική μέθοδος για τη μοντελοποίηση του σκοτεινού υγρού,αλλά προς το παρόν απαιτεί πάρα πολλά σημεία δεδομένων παρατήρησης για να είναι εφικτοί οι υπολογισμοί και δεν υπάρχουν αρκετά σημεία δεδομένων στους κοσμολόγους.Ένα βήμα απλοποίησης πραγματοποιήθηκε με μοντελοποίηση της υπόθεσης μέσω μοντέλων βαθμών πεδίου αντ' αυτού,όπως γίνεται σε άλλες εναλλακτικές προσεγγίσεις για τη σκοτεινή ενέργεια και τη σκοτεινή ύλη.</span></div><p></p>ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.com0tag:blogger.com,1999:blog-6644102595821010388.post-29559015074250046612020-11-21T12:43:00.005-08:002021-05-18T06:12:28.740-07:00ΦΩΤΙΝΟ<p style="text-align: justify;"><span style="color: red; font-family: verdana; font-size: x-large;"><b>ΦΩΤΙΝΟ</b></span></p><p style="text-align: justify;"></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXNdInSC4p2LC0QCepzdM1hVFkfJ-OY5F4Qy_-OdvStIeq1WVZuVohUVtFblxeeFG1gePPvpuF7vdBRNJALKgzUPUNcsWMnwTDlLzChYmt8W2epDbhUMR_dzauzwD7RkfT8H_OTsp2hAg/s200/%25CE%25A6%25CE%25A9%25CE%25A4%25CE%259F%25CE%25A4%25CE%2599%25CE%259D%25CE%259F2.gif" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="112" data-original-width="200" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXNdInSC4p2LC0QCepzdM1hVFkfJ-OY5F4Qy_-OdvStIeq1WVZuVohUVtFblxeeFG1gePPvpuF7vdBRNJALKgzUPUNcsWMnwTDlLzChYmt8W2epDbhUMR_dzauzwD7RkfT8H_OTsp2hAg/w400-h224/%25CE%25A6%25CE%25A9%25CE%25A4%25CE%259F%25CE%25A4%25CE%2599%25CE%259D%25CE%259F2.gif" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><span style="color: #800180; font-family: verdana; font-size: large;">ΦΩΤΙΝΟ</span></b></td></tr></tbody></table><p></p><div style="text-align: justify;"><b style="color: red; font-family: verdana;">ΕΙΣΑΓΩΓΗ</b><br /><span style="font-family: verdana;"><br /></span></div><div style="text-align: justify;"><span style="font-family: verdana;"> <b><span style="color: #2b00fe;">Φωτίνο</span> ονομάζεται ένα υποθετικό υποατομικό σωματίδιο,φερμόνιο WIMP υπεύθυνο της δημιουργίας του φωτονίου που προβλέπεται από την θεωρία της υπερσυμμετρίας.</b></span></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7AW7b-v5h7LRceyr2u2CJiHhDCLxVkPWHvWmK9mOCWgCDAsKIrYiXxczM2eiE6eXfvad0AVLERMz9EG7IXXvDsQV3sijm3sbz3edgvRpGGCSH8bfUGnsplPvV4SoX5GUtAcIJSCJ-4Ow/s850/%25CE%25A6%25CE%25A9%25CE%25A4%25CE%259F%25CE%25A4%25CE%2599%25CE%259D%25CE%259F.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="409" data-original-width="850" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7AW7b-v5h7LRceyr2u2CJiHhDCLxVkPWHvWmK9mOCWgCDAsKIrYiXxczM2eiE6eXfvad0AVLERMz9EG7IXXvDsQV3sijm3sbz3edgvRpGGCSH8bfUGnsplPvV4SoX5GUtAcIJSCJ-4Ow/w640-h308/%25CE%25A6%25CE%25A9%25CE%25A4%25CE%259F%25CE%25A4%25CE%2599%25CE%259D%25CE%259F.png" width="640" /></a></td></tr></tbody></table><p></p><h1 class="nova-e-text nova-e-text--size-m nova-e-text--family-sans-serif nova-e-text--spacing-none nova-e-text--color-inherit" itemprop="caption" style="background-color: white; line-height: 1.3; margin-bottom: 0px; margin-top: 0px; text-align: justify;"><span style="color: #800180; font-family: verdana; font-size: small;"><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">Διαγράμματα που αντιστοιχούν σε (α) ανταλλαγή φωτονίων και (β) </span></span>ανταλλαγή <span style="vertical-align: inherit;"> φωτίνων.</span><span style="vertical-align: inherit;">Τα σωματίδια momenta συμβολίζονται με παρένθεση</span></span></h1><div style="text-align: justify;"><span style="font-family: verdana;"> Πρόκειται για ένα παράδειγμα του υποατομικού σωματιδίου <b>γκατζίνο</b>.</span></div><div style="text-align: justify;"><span style="color: red; font-family: verdana;"><span style="color: black;"><br /></span></span><b style="color: red; font-family: verdana;">ΧΑΡΑΚΤΗΡΙΣΤΙΚΑ ΤΩΝ ΦΩΤΟΤΙΝΩΝ</b><span style="font-family: verdana;"><br /></span><span style="font-family: verdana;"><span style="color: red;"><b><br /></b></span></span></div><div style="text-align: justify;"><span style="font-family: verdana;"><span style="color: red;"><b> </b></span>Παρόλο που μέχρι στιγμής δεν έχει παρατηρηθεί κανένα φωτίνο,είναι ένα από τα υποψήφια σωματίδια για το ελαφρύτερο υπερσυμμετρικό σωματίδιο στο σύμπαν.</span></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIqizJLMUgLSxuWy0mtbiXjOLg3ICxaKGOEa_URtbnEKW3U0NXwYLCBJZuBckY2eI-iiu72nXcnQ_ZOsCobVEBz_plAOyO-H3gOXKsl2Fd4BVaUgktvCmbhG8MXGP9zm1zMcEE9vveoxg/s850/%25CE%25A6%25CE%25A9%25CE%25A4%25CE%259F%25CE%25A4%25CE%2599%25CE%259D%25CE%259F3.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="603" data-original-width="850" height="454" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIqizJLMUgLSxuWy0mtbiXjOLg3ICxaKGOEa_URtbnEKW3U0NXwYLCBJZuBckY2eI-iiu72nXcnQ_ZOsCobVEBz_plAOyO-H3gOXKsl2Fd4BVaUgktvCmbhG8MXGP9zm1zMcEE9vveoxg/w640-h454/%25CE%25A6%25CE%25A9%25CE%25A4%25CE%259F%25CE%25A4%25CE%2599%25CE%259D%25CE%259F3.png" width="640" /></a></td></tr></tbody></table><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td class="tr-caption" style="text-align: center;"><h1 class="nova-e-text nova-e-text--size-m nova-e-text--family-sans-serif nova-e-text--spacing-none nova-e-text--color-inherit" itemprop="caption" style="background-color: white; line-height: 1.3; margin-bottom: 0px; margin-top: 0px; text-align: justify;"><span style="color: #800180; font-family: verdana; font-size: small; vertical-align: inherit;">Κανόνες Feynman για αλληλεπίδραση ηλεκτρονίων-φωτίνων και πολλαπλασιαστών φωτονίων</span></h1></td></tr></tbody></table><p style="text-align: justify;"><span style="font-family: verdana;"> Η παραγωγή </span><span style="font-family: verdana;">φωτίνων γίνεται</span><span style="font-family: verdana;"> από πηγές κοσμικών ακτίνων εξαιρετικά υψηλής ενέργειας.</span><span style="font-family: verdana;"><span style="background-color: white; text-align: left;">Η</span><span style="background-color: white; text-align: left;"> μάζα του θα μπορούσε να κυμαίνεται από <b>50</b> έως <b>1.000 φορές </b>εκείνες του πρωτονίου.</span></span></p><table class="infobox" style="background-color: #f8f9fa; border-spacing: 3px; border: 1px solid rgb(162, 169, 177); clear: right; line-height: 1.5em; margin: 0.5em 0px 0.5em 1em; padding: 0.2em; width: 22em;"><caption style="padding: 0.2em;"><span style="font-family: verdana; vertical-align: inherit;"><b> <span style="color: red;">Φωτίνο</span></b></span></caption><tbody style="color: black;"><tr><th scope="row" style="text-align: left; vertical-align: top;"><span style="color: #2b00fe; font-family: verdana;">Σύνθεση</span></th><td style="vertical-align: top;"><b><span style="font-family: verdana;"> Στοιχειώδες σωματίδιο</span></b></td></tr><tr><th scope="row" style="text-align: left; vertical-align: top;"><span style="color: #2b00fe; font-family: verdana;">Στατιστική</span></th><td style="vertical-align: top;"><b><span style="font-family: verdana;"> Φερμιόνιο</span></b></td></tr><tr><th scope="row" style="text-align: left; vertical-align: top;"><span style="color: #2b00fe; font-family: verdana;">Αλληλεπιδράσεις</span></th><td style="vertical-align: top;"><b><span style="font-family: verdana;"> Ηλεκτρομαγνητικός</span></b></td></tr><tr><th scope="row" style="text-align: left; vertical-align: top;"><span style="vertical-align: inherit;"><span style="color: #2b00fe; font-family: verdana; vertical-align: inherit;">Κατάσταση</span></span></th><td style="vertical-align: top;"><span style="vertical-align: inherit;"><span style="font-family: verdana; vertical-align: inherit;"><b> Υποθετικός</b></span></span></td></tr><tr><th scope="row" style="text-align: left; vertical-align: top;"><span style="vertical-align: inherit;"><span style="color: #2b00fe; font-family: verdana; vertical-align: inherit;">Σύμβολο</span></span></th><td style="vertical-align: top;"><span style="white-space: nowrap;"><b><span style="font-family: verdana; font-size: medium;"><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">γ͂</span></span><span style="display: inline-block; line-height: 1em; margin-bottom: -0.3em; vertical-align: 0.8em;"><span style="line-height: inherit; vertical-align: baseline;"></span><br /><span style="line-height: inherit; vertical-align: baseline;"></span></span></span></b></span></td></tr><tr><th scope="row" style="text-align: left; vertical-align: top;"><span style="color: #2b00fe; font-family: verdana;">Ηλεκτρικό φορτίο</span></th><td style="vertical-align: top;"><b><span style="font-family: verdana;"><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">0 </span></span><i>ε</i></span></b></td></tr><tr><th scope="row" style="text-align: left; vertical-align: top;"><span style="color: #2b00fe; font-family: verdana;">σπίν</span></th><td style="vertical-align: top;"><span style="vertical-align: inherit;"><span style="font-family: verdana; vertical-align: inherit;"><b>1/2</b></span></span></td></tr></tbody></table><div style="text-align: justify;"><span style="color: red; font-family: verdana;"><b>ΑΡΙΘΜΟΙ ΦΩΤΟΤΙΝΩΝ</b></span></div><div style="text-align: justify;"><span style="color: red; font-family: verdana;"><b><br /></b></span><span style="font-family: verdana;"> Τα <b>φωτίνα</b> έχουν <b>λεπτονικό αριθμό 0</b>,<b>βαρυονικό αριθμό 0</b>,και <b>σπιν 1/2</b>.Με <b>R-parity −1</b> είναι πιθανό υποψήφιο σωματίδιο για σκοτεινή ύλη.Αναμιγνύεται με τους υπερ-συμμετέχοντες του <b>Z μποζονίου (zino)</b> και των ουδέτερων <b>higgs (higgsino) </b>για να σχηματίσει το ουδέτερο.</span></div>ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.com0tag:blogger.com,1999:blog-6644102595821010388.post-37636163040037622682018-11-25T14:28:00.000-08:002020-09-12T09:54:51.642-07:00ΒΡΑΒΕΙΟ ΝΟΜΠΕΛ ΦΥΣΙΚΗΣ<div dir="ltr" style="text-align: left;" trbidi="on">
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<b style="color: red; font-family: verdana, sans-serif;"><span style="font-size: x-large;">ΒΡΑΒΕΙΟ ΝΟΜΠΕΛ ΦΥΣΙΚΗΣ<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVJ93s3iJOVkfqzX7xOxJ5WwSHhQ-hamkxphuirD9Wvadb9m2oHQbST0t1xF2vvfeWT1BHssDOou2U7S0ny66k4rMxG4Mj2nmXDqrjg68HgFlMpJqwWo_DT27Z23Ac4jh77yHS0mUFu90/s1600/%25CE%2592%25CE%25A1%25CE%2591.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="149" data-original-width="149" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVJ93s3iJOVkfqzX7xOxJ5WwSHhQ-hamkxphuirD9Wvadb9m2oHQbST0t1xF2vvfeWT1BHssDOou2U7S0ny66k4rMxG4Mj2nmXDqrjg68HgFlMpJqwWo_DT27Z23Ac4jh77yHS0mUFu90/s200/%25CE%2592%25CE%25A1%25CE%2591.gif" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-size: large;">ΒΡΑΒΕΙΟ ΝΟΜΠΕΛ ΦΥΣΙΚΗΣ</span></b></td></tr>
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<b style="color: red; font-family: verdana, sans-serif;">ΠΕΡΙΕΧΟΜΕΝΑ</b><br />
<span style="font-size: x-small;"><span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b><br /></b></span><span style="font-family: "verdana" , sans-serif;"><span class="Apple-style-span" style="color: red;"><b><a href="http://physiclessons.blogspot.com/2012/03/blog-post.html?utm_source=BP_recent">ΒΡΑΒΕΙΟ ΝΟΜΠΕΛ ΦΥΣΙΚΗΣ ΕΙΣΑΓΩΓΗ</a></b></span></span></span><br />
<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><span class="Apple-style-span" style="color: red;"><b><a href="http://physiclessons.blogspot.com/2012/03/blog-post_18.html">ΕΠΙΛΟΓΗ ΓΙΑ ΒΡΑΒΕΙΟ ΝΟΜΠΕΛ</a></b></span></span><br />
<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><span class="Apple-style-span" style="color: red;"><b><a href="http://physiclessons.blogspot.com/2012/03/blog-post_8183.html">ΒΡΑΒΕΙΑ ΕΝΟΣ ΝΟΜΠΕΛΙΣΤΑ ΦΥΣΙΚΟΥ</a></b></span></span><br />
<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><b><a href="http://physiclessons.blogspot.com/2012/03/blog-post_4325.html">ΤΕΛΕΤΗ ΑΠΟΝΟΜΗΣ ΒΡΑΒΕΙΩΝ ΝΟΜΠΕΛ ΦΥΣΙΚΗΣ</a></b></span><br />
<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><b><a href="http://physiclessons.blogspot.com/2012/03/blog-post_9305.html">Η ΕΠΙΤΡΟΠΗ ΝΟΜΠΕΛ ΓΙΑ ΤΗ ΦΥΣΙΚΗ</a></b></span><br />
<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><b><a href="http://physiclessons.blogspot.com/2012/03/blog-post_6592.html">ΒΑΣΙΛΙΚΗ ΣΟΥΗΔΙΚΗ ΑΚΑΔΗΜΙΑ ΕΠΙΣΤΗΜΩΝ</a></b></span><br />
<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><b><a href="http://physiclessons.blogspot.com/2012/03/blog-post_568.html">ΑΡΙΘΜΟΣ ΒΡΑΒΕΙΩΝ ΝΟΜΠΕΛ ΣΤΗ ΦΥΣΙΚΗ</a></b></span><br />
<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><b><a href="http://physiclessons.blogspot.com/2012/03/blog-post_8135.html">ΝΟΜΠΕΛΙΣΤΕΣ ΦΥΣΙΚΟΙ</a></b></span><br />
<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><b><a href="http://physiclessons.blogspot.com/2012/03/blog-post_9997.html">ΟΙ ΜΕΓΑΛΟΙ ΝΙΚΗΤΕΣ ΒΡΑΒΕΙΟΥ ΝΟΜΠΕΛ ΦΥΣΙΚΗΣ</a></b></span><br />
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<b style="font-family: verdana, sans-serif;"> Το <span style="color: blue;">Βραβείο Νόμπελ Φυσικής </span> απονέμεται μία φορά το χρόνο από τη Βασιλική Σουηδική Ακαδημία Επιστημών.</b><br />
<b style="font-family: verdana, sans-serif;"> </b><span style="font-family: verdana, sans-serif;">Είναι ένα από τα πέντε</span><b style="font-family: verdana, sans-serif;"> βραβεία Νόμπελ </b><span style="font-family: verdana, sans-serif;">που συστάθηκε με το θέλημα του </span><b style="font-family: verdana, sans-serif;">Άλφρεντ Νόμπελ</b><span style="font-family: verdana, sans-serif;"> το </span><b style="font-family: verdana, sans-serif;">1895 </b><span style="font-family: verdana, sans-serif;">και απονέμεται από το </span><b style="font-family: verdana, sans-serif;">1901.</b><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px;"><b><span class="Apple-style-span" style="color: purple;">Ο Άλφρεντ Νόμπελ</span></b></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> </b>Οι άλλες είναι το βραβείο <b>Νόμπελ Χημείας,Βραβείο Νόμπελ Λογοτεχνίας,Βραβείο Νόμπελ Ειρήνης </b>και<b> βραβείο Νόμπελ Φυσιολογίας</b> ή <b>Ιατρικής</b>.Το </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">πρώτο<b> Βραβείο Νόμπελ Φυσικής</b> απονεμήθηκε στον<b> </b></span><span style="font-family: "verdana" , sans-serif;"><b>Γερμανό </b></span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b>Βίλχελμ Ρέντγκεν</b> «σε αναγνώριση της εξαιρετικής υπηρεσίες που έχει προσφέρει από την </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">ανακάλυψη των <b>ακτίνων X</b>.</span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">"Αυτό το βραβείο χορηγείται από το <b>Ίδρυμα Νόμπελ </b>και θεωρείται ευρέως ως το πιο σημαντικό βραβείο που ένας επιστήμονας μπορεί να λάβει στη </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">φυσική.Παρουσιάζεται στη <b>Στοκχόλμη</b>,ενώ η ετήσια τελετή στις <b>10 Δεκεμβρίου</b>,η επέτειος του θανάτου του <b>Νόμπελ</b>.<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
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<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-size: small;">Η πρώτη σελίδα της χειρόγραφης διαθήκης του Άλφρεντ Νόμπελ με την υπογραφή του</span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Ο<b> Άλφρεντ Νόμπελ </b>ζητούσε στην διαθήκη του ότι τα χρήματά του να χρησιμοποιηθούν για να δημιουργήσουν μια σειρά από βραβεία για αυτούς που παρέχουν το "μεγαλύτερο όφελος για την ανθρωπότητα" στη<b> Φυσική</b>,στη<b> Χημεία</b>,στην<b> Ειρήνη</b>,στη<b> Φυσιολογία</b> ή στην<b> Ιατρική</b>,και στη <b>Λογοτεχνία.</b> </span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Αν και ο <b>Άλφρεντ Νόμπελ</b> έγραψε πολλές διαθήκες κατά τη διάρκεια της ζωής του,η τελευταία διαθήκη γράφτηκε ένα χρόνο πριν πεθάνει,και την υπέγραψε στο <b>Σουηδικό-νορβηγικό Club</b> στο <b>Παρίσι</b> στις <b>27 Νοεμβρίου 1895</b>.Ο <b>Άλφρεντ Νόμπελ</b> κληροδότησε το <b>94%</b> του το σύνολο του ενεργητικού,<b>31 εκατομμύρια σουηδικές κορώνες (186 εκατομμύρια </b></span><span style="font-family: "verdana" , sans-serif;"><b>$</b></span><span style="font-family: "verdana" , sans-serif;"><b> το 2008)</b>,να καθιερώσει τα πέντε <b>βραβεία Νόμπελ</b>.Λόγω του επιπέδου του σκεπτικισμού που την περιβάλλει εγκρίθηκε την<b> 26 Απριλίου</b> του<b> 1897</b> από το νορβηγικό κοινοβούλιο.Οι εκτελεστές της διαθήκης του ήταν ο <b>Ragnar Sohlman</b> και ο <b>Rudolf Lilljequist,</b>οι οποίοι διαμόρφωσαν το <b>Ίδρυμα Νόμπελ</b>,για τη φροντίδα της περιουσίας του<b> Νόμπελ </b>και για να οργανώσουν τα βραβεία.</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB93H8RZ-RFOfDsOw-dvYbLnEtnmdU_Qig1XT14KuODZg1gmqydYAIvWxIYCvBdeRJSkmSjNE-EDGLu3q_HdPCJNj3O-Bj72SNqxJKVw7B29gm5BtISrFo0eWtU7gN6CIUKtmtyEL5Wq0/s1600/%25CE%2592%25CE%25A1%25CE%25912.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="190" data-original-width="266" height="285" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiB93H8RZ-RFOfDsOw-dvYbLnEtnmdU_Qig1XT14KuODZg1gmqydYAIvWxIYCvBdeRJSkmSjNE-EDGLu3q_HdPCJNj3O-Bj72SNqxJKVw7B29gm5BtISrFo0eWtU7gN6CIUKtmtyEL5Wq0/s400/%25CE%2592%25CE%25A1%25CE%25912.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-family: Verdana, sans-serif; font-size: small;">Η πρώτη τελετή απονομής των βραβείων Νόμπελ στη Βασιλική Ακαδημία Μουσικής στη Στοκχόλμη.Στο μέσον διακρίνεται ο Röntgen τη στιγμή που παραλαμβάνει το βραβείο για τη Φυσική</span></b></td></tr>
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<span style="font-family: verdana, sans-serif;"> Το βραβείο που απονέμει τον τίτλο οργανισμών ακολουθείται:Το </span><b style="font-family: verdana, sans-serif;">Ινστιτούτου Καρολίνσκα </b><span style="font-family: verdana, sans-serif;">της στις </span><b style="font-family: verdana, sans-serif;">7 Ιουνίου,</b><span style="font-family: verdana, sans-serif;">η</span><b style="font-family: verdana, sans-serif;"> Σουηδική Ακαδημία </b><span style="font-family: verdana, sans-serif;">στις </span><b style="font-family: verdana, sans-serif;">9 Ιουνίου,και η Βασιλική Σουηδική Ακαδημία των Επιστημών </b><span style="font-family: verdana, sans-serif;">στις </span><b style="font-family: verdana, sans-serif;">11 Ιουνίου.</b><span style="font-family: verdana, sans-serif;">Το</span><b style="font-family: verdana, sans-serif;"> Ίδρυμα Νόμπελ,</b><span style="font-family: verdana, sans-serif;">στη συνέχεια,φτάνει σε συμφωνία σχετικά με τις κατευθυντήριες γραμμές για το πώς το </span><b style="font-family: verdana, sans-serif;">Βραβείο Νόμπελ </b><span style="font-family: verdana, sans-serif;">θα πρέπει να απονέμεται.Το </span><b style="font-family: verdana, sans-serif;">1900</b><span style="font-family: verdana, sans-serif;">,δημιουργήθηκε πρόσφατα το καταστατικό του</span><b style="font-family: verdana, sans-serif;"> Ιδρύματος Νόμπελ</b><span style="font-family: verdana, sans-serif;"> και διακηρύχθηκε από τον </span><b style="font-family: verdana, sans-serif;">βασιλιά Oscar II.</b><span style="font-family: verdana, sans-serif;">Σύμφωνα με τη διαθήκη του </span><b style="font-family: verdana, sans-serif;">Νόμπελ</b><span style="font-family: verdana, sans-serif;">,η </span><b style="font-family: verdana, sans-serif;">Βασιλική Σουηδική Ακαδημία των Επιστημών</b><span style="font-family: verdana, sans-serif;"> θα απονείμει το βραβείο στη </span><b style="font-family: verdana, sans-serif;">Φυσική.</b></div>
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<b style="color: red; font-family: Verdana, sans-serif; line-height: 16px; text-align: justify;">ΕΠΙΛΟΓΗ ΓΙΑ ΒΡΑΒΕΙΟ ΝΟΜΠΕΛ</b></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> </b>Το πολύ τρεις νομπελίστες και δύο διαφορετικά έργα μπορεί να επιλεγούν για το<b> Βραβείο Νόμπελ Φυσικής</b>.Σε σύγκριση με κάποια άλλα <b>βραβεία Νόμπελ</b>,το διορισμό και τη διαδικασία επιλογής για το βραβείο στη <b>Φυσική</b> είναι μακρά και αυστηρή.Αυτός είναι ένας βασικός λόγος που έχει αποκτήσει μεγαλύτερη σημασία και έχει γίνει το πιο σημαντικό βραβείο στη <b>Φυσική</b>.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> </b>Οι<b> Νομπελίστες </b>επιλέγονται από την<b> Επιτροπή Νόμπελ </b>για τη<b> Φυσική</b>,μια επιτροπή<b> Νόμπελ </b>που αποτελείται από πέντε μέλη που εκλέγονται από τη <b>Βασιλική Σουηδική Ακαδημία Επιστημών.</b>Στο πρώτο στάδιο,πολλές χιλιάδες άνθρωποι καλούνται να προτείνουν υποψήφιους.Αυτά τα ονόματα ελέγχονται και θα συζητηθεί από τους εμπειρογνώμονες μέχρι να γίνει η επιλογή.</span></div>
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<strong><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Στην φωτογραφία αυτή βλέπουμε τους 29 Φυσικούς που συμμετείχαν στην πέμπτη διάσκεψη του Solvay στις Βρυξέλλες το 1927.Η πέμπτη αυτή σύνοδος είναι η πιο γνωστή από όλες τις υπόλοιπες γιατί οι φυσικοί είχαν συγκεντρωθεί για να αναλύσουνε θέματα για τα ηλεκτρόνια και τα φωτόνια και να συζητήσουν την πρόσφατη διατυπομένη κβαντική θεωρία.Να τονίσουμε ότι οι 17 από τους εικονιζόμενους πήραν βραβείο Νόμπελ.Εικονίζονται οι μεγαλύτεροι Φυσικοί της ανθρωπότητας</span></strong></div>
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<strong><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Στην Πρώτη Σειρά:I. Langmuir,Max Planck,Marie Curie,Hendrik Antoon lorentz,Albert Einstein,P. Langevin,Ch. E. Guye,C.T.R. Wilson,O.W. Richardson</span></strong></div>
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<strong><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Στη Μεσαία Σειρά:P. Debye,M. Knudsen,William L. Bragg,H.A. Kramers,Paul dirac,A.H. Compton, Louis de Broglie,Max Born,Niels Bohr</span></strong></div>
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<strong><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Στην Πίσω Σειρά:A. Piccard,E. Henriot,P. Ehrenfest,Ed. Herzen,Th. De Bonder,Erwin Scrondinger,E. Verschaffelt,Wolfgang Pauli,Werner Heisenberg,R.H. Fowler,L. Brillouin.</span></strong><span style="font-family: "lucida grande" , "tahoma" , "verdana" , "arial" , sans-serif; font-size: 11px;"> </span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> </b>Τα έντυπα αποστέλλονται σε περίπου τρεις χιλιάδες άτομα και να τους καλούν να υποβάλουν υποψηφιότητες.Τα ονόματα των υποψηφίων δεν έχουν ποτέ </span><span style="font-family: "verdana" , sans-serif;">ανακοινωθεί </span><span style="font-family: "verdana" , sans-serif;">δημοσίως.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Οι υποψηφιότητες εξετάζονται από την επιτροπή,καθώς και ο κατάλογος παράγεται από διακόσιους περίπου υποψηφίους.Ο κατάλογος διαβιβάζεται στους επιλεγμένους εμπειρογνώμονες σε κάθε τομέα.Έτσι περιορίζονται σε περίπου δεκαπέντε ονόματα.Η επιτροπή υποβάλλει έκθεση με συστάσεις προς το κατάλληλο όργανο.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Ενώ δεν επιτρέπονται μεταθανάτιες υποψηφιότητες,τα βραβεία μπορεί να δοθούν αν το άτομο πεθάνει κατά τους μήνες μεταξύ της αποφάσεως της <b>Επιτροπής Απονομής Βραβείου </b>(συνήθως τον <b>Οκτώβριο</b>) και της τελετής του <b>Δεκεμβρίου</b>.Πριν από το <b>1974</b>,μεταθανάτια βραβεία επιτρεπόταν αν ο δικαιούχος είχε πεθάνει,αφού είχε υποβάλει υποψηφιότητά.</span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Το <b>Βραβείο Νόμπελ Φυσικής </b>προϋποθέτει ότι τα επιτεύγματα που αναγνωρίζονται έχουν <b>«δοκιμαστεί με το χρόνο"</b>.Στην πράξη αυτό σημαίνει ότι η απόκλιση μεταξύ της ανακάλυψης και του βραβείου είναι συνήθως της τάξης των <b>20 ετών</b> και μπορεί να είναι πολύ περισσότερο.Για παράδειγμα,το μισό </span><span style="font-family: "verdana" , sans-serif;">του βραβείου <b>Νόμπελ Φυσικής</b> </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">το <b>1983 </b>απονεμήθηκε στον <b>Subrahmanyan Chandrasekhar </b>για την εργασία του για την <b>αστρική δομή και την εξέλιξη </b>που έγινε κατά τη διάρκεια της δεκαετίας του <b>1930.</b>Ως μειονέκτημα αυτής της προσέγγισης,είναι ότι δεν ζουν αρκετό καιρό </span><span style="font-family: "verdana" , sans-serif;">όλοι οι επιστήμονες </span><span style="font-family: "verdana" , sans-serif;">για να αναγνωριστεί το έργο τους. </span><br />
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<span style="color: red; font-family: "verdana" , sans-serif;"><b>ΒΡΑΒΕΙΑ ΕΝΟΣ ΝΟΜΠΕΛΙΣΤΑ ΦΥΣΙΚΟΥ</b></span></div>
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<span style="font-family: verdana, sans-serif;"><span style="color: red; font-size: medium; font-weight: bold;"> </span>Ένας </span><span style="font-family: verdana, sans-serif;"><b>Φυσικός Νομπελίστας</b> κερδίζει ένα χρυσό μετάλλιο,ένα δίπλωμα που φέρει μια παραπομπή </span><span style="font-family: verdana, sans-serif;">που αναγράφεται το αιτιολογικό της απονομής</span><span style="font-family: verdana, sans-serif;">,και ένα χρηματικό ποσό</span><span style="font-family: "verdana" , sans-serif;">.</span><br />
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<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Η τελετή απονομής Βραβείου Νόμπελ Φυσικής</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Το ποσό των χορηγούμενων χρημάτων εξαρτάται από τα εισοδήματα του </span><b style="font-family: verdana, sans-serif;">Ιδρύματος Νόμπελ</b><span style="font-family: "verdana" , sans-serif;"> εκείνο το έτος.Εάν ένα βραβείο απονέμεται σε περισσότερα από ένα βραβευμένους,τα χρήματα είτε να μοιραστούν ισόποσα μεταξύ τους ή,για τρεις βραβευθέντες,αυτό μπορεί να χωριστεί σε ένα δεύτερο έως δύο τρίτα.Εάν ένα βραβείο απονέμεται από κοινού σε δύο ή περισσότερα βραβευθέντες,τα χρήματα είναι χωρισμένα μεταξύ τους.</span></div>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΤΟ ΒΡΑΒΕΙΟ ΝΟΜΠΕΛ ΜΕΤΑΛΛΙΟ</b></span><br />
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<span style="font-family: verdana, sans-serif;"><span style="color: red; font-weight: bold;"> </span>Τα </span><span style="font-family: verdana, sans-serif;">μετάλλια </span><span style="font-family: verdana, sans-serif;">βραβεία</span><b style="font-family: verdana, sans-serif;"> Νόμπελ</b><span style="font-family: verdana, sans-serif;">,κόβονται στη</span><b style="font-family: verdana, sans-serif;"> Σουηδία </b><span style="font-family: verdana, sans-serif;">από το </span><b style="font-family: verdana, sans-serif;">Νομισματοκοπείο </b><span style="font-family: verdana, sans-serif;">της</span><b style="font-family: verdana, sans-serif;"> Νορβηγίας </b><span style="font-family: verdana, sans-serif;">από το</span><b style="font-family: verdana, sans-serif;"> 1902</b><span style="font-family: verdana, sans-serif;">,και επιβλέπονται από το</span><b style="font-family: verdana, sans-serif;"> Ίδρυμα Νόμπελ.</b></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPTeyMJyHAK5YAsqnfMDJq-Ja4gbj54UUtHkoHtydcbqSiD36di-t7U6fpJ5DBkpkYoENqM_o2T3blUbGoAvX7IUCMCe68aDqBxa_an0NtXN0LcrAhS9sjZmL_ItsMw-X-lAAI5r8uLlLt/s1600/%25CE%2592%25CE%25A1%25CE%2591%25CE%2592%25CE%2595%25CE%2599%25CE%259F+%25CE%259D%25CE%259F%25CE%259C%25CE%25A0%25CE%2595%25CE%259B+%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597%25CE%25A3%25281%2529.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "verdana" , sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPTeyMJyHAK5YAsqnfMDJq-Ja4gbj54UUtHkoHtydcbqSiD36di-t7U6fpJ5DBkpkYoENqM_o2T3blUbGoAvX7IUCMCe68aDqBxa_an0NtXN0LcrAhS9sjZmL_ItsMw-X-lAAI5r8uLlLt/s1600/%25CE%2592%25CE%25A1%25CE%2591%25CE%2592%25CE%2595%25CE%2599%25CE%259F+%25CE%259D%25CE%259F%25CE%259C%25CE%25A0%25CE%2595%25CE%259B+%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597%25CE%25A3%25281%2529.png" /></span></a></td></tr>
<tr><td class="tr-caption"><span style="font-size: small;"><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; line-height: 16px;"><b><span class="Apple-style-span" style="color: purple;">Το </span></b></span><b style="font-family: verdana, sans-serif;"><span class="Apple-style-span" style="color: purple;">μετάλλιο</span></b><b style="font-family: verdana, sans-serif;"><span class="Apple-style-span" style="color: purple;"> βραβείο Νόμπελ </span></b></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> </b>Κάθε μετάλλιο έχει μια εικόνα του <b>Alfred Nobel </b>στο αριστερό προφίλ στην εμπρόσθια όψη (μπροστινή όψη του νομίσματος).Το <b>βραβείο Νόμπελ </b>μετάλλιο της <b>Φυσικής</b>,της <b>Χημείας</b>,της <b>Φυσιολογίας</b> ή της <b>Ιατρικής,</b>της <b>Λογοτεχνίας </b>δείχνουν την εικόνα του <b>Alfred Nobel</b> και τα χρόνια της γέννησης και του θανάτου του <b>(1833-1896)</b>.</span></div>
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<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Οι δυο όψεις του μεταλλίου</span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Πορτρέτο του <b>Νόμπελ </b>εμφανίζεται επίσης στην εμπρόσθια όψη του </span><span style="font-family: "verdana" , sans-serif;">μεταλλίου </span><b style="font-family: verdana, sans-serif;">Νόμπελ Ειρήνης </b><span style="font-family: "verdana" , sans-serif;">και το μετάλλιο για το βραβείο στα </span><b style="font-family: verdana, sans-serif;">Οικονομικά</b><span style="font-family: "verdana" , sans-serif;">,αλλά με ελαφρώς διαφορετικό σχεδιασμό.Η εικόνα στο πίσω μέρος ενός μεταλλίου ποικίλλει ανάλογα με το ίδρυμα που χορηγεί το βραβείο.Η αντίστροφη πλευρά των μεταλλίων του </span><b style="font-family: verdana, sans-serif;">βραβείο Νόμπελ</b><span style="font-family: "verdana" , sans-serif;"> </span><b style="font-family: verdana, sans-serif;">Χημείας</b><span style="font-family: "verdana" , sans-serif;"> και </span><b style="font-family: verdana, sans-serif;">Φυσικής</b><span style="font-family: "verdana" , sans-serif;"> μοιράζονται την ίδια σχεδίαση.</span></div>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΤΟ ΔΙΠΛΩΜΑ ΝΟΜΠΕΛ ΦΥΣΙΚΗΣ</b></span><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> </b>Οι<b> Νομπελίστες</b> λαμβάνουν ένα δίπλωμα απευθείας από τα χέρια του βασιλιά της<b> Σουηδίας</b>.Κάθε δίπλωμα είναι μοναδικά σχεδιασμένο από το ίδρυμα για το <b>Νόμπελ </b>που λαμβάνει.</span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px;"><b><span class="Apple-style-span" style="color: purple;">Το δίπλωμα</span></b></span></td></tr>
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<b style="font-family: verdana, sans-serif;"> </b><span style="font-family: "verdana" , sans-serif;">Το δίπλωμα που περιέχει μια εικόνα και κείμενο το οποίο αναφέρει το όνομα του</span><b style="font-family: verdana, sans-serif;"> Νόμπελ </b><span style="font-family: "verdana" , sans-serif;">και παραπομπή γιατί πιο λόγω έλαβαν το βραβείο.</span></div>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΧΡΗΜΑΤΙΚΟ ΒΡΑΒΕΙΟ</b></span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Στο βραβευμένο δίνεται επίσης ένα χρηματικό ποσό όταν λαμβάνει το βραβείο <b>Νόμπελ,</b>με επιταγή που επιβεβαιώνει το ποσό.Το <b>2009</b>,το χρηματικό ποσό ήταν <b>10 εκατ. SEK (1,4 εκατ. </b></span><b><span style="font-family: "verdana" , sans-serif;">$ </span><span style="font-family: "verdana" , sans-serif;">ΗΠΑ</span></b><span style="font-family: "verdana" , sans-serif;"><b>).</b>Το ποσό μπορεί να διαφέρει ανάλογα τα πόσα χρήματα μπορεί να χορηγεί </span><span style="font-family: "verdana" , sans-serif;">το<b> Ίδρυμα Νόμπελ</b></span><span style="font-family: "verdana" , sans-serif;"> </span><span style="font-family: "verdana" , sans-serif;">το συγκεκριμένο έτος.</span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><b>Στο βραβευμένο δίνεται επίσης ένα χρηματικό ποσό</b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Εάν υπάρχουν δύο νικητές σε μια συγκεκριμένη κατηγορία,το επιδοτούμενο χρηματικό βραβείο κατανέμεται ισόποσα μεταξύ των δικαιούχων.Εάν υπάρχουν τρεις,η αναθέτουσα επιτροπή έχει τη δυνατότητα της διαίρεσης της επιχορήγησης εξίσου,ή τη χορήγηση κατά το ήμισυ στον έναν παραλήπτη και ένα τέταρτο στους άλλους δύο.</span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Αν ο βραβευόμενος αποποιηθεί ή δεν παραλάβει το βραβείο του μέσα σε ορισμένη προθεσμία,το χρηματικό ποσό επιστρέφεται στο ίδρυμα.Σε μερικές περιπτώσεις,οι κυβερνήσεις μερικών χωρών με ολοκληρωτικά ή αυταρχικά καθεστώτα,έχουν απαγορεύσει στον βραβευμένο να δεχθεί το <b>Βραβείο Νόμπελ</b>.Παρ' όλα αυτά,ο βραβευμένος καταχωρίζεται στη βίβλο των κατόχων <b>Βραβείων Νόμπελ</b>,με την παρατήρηση<b> «δεν αποδέχθηκε το βραβείο»</b>.</span><br />
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΤΕΛΕΤΗ ΑΠΟΝΟΜΗΣ ΒΡΑΒΕΙΩΝ ΝΟΜΠΕΛ ΦΥΣΙΚΗΣ</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b> </b>Η επιτροπή και το ίδρυμα που ενεργεί ως επιτροπή επιλογής για το βραβείο ανακοινώνει συνήθως τα ονόματα των επιτυχόντων,τον <b>Οκτώβριο.</b></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCFv-VqiSYN_Zd0hesrZ_JvtzSrX2mj2wO6PrA1nLzjhGHxnyJLsXT7zIzMLkp_q5hCb-G1XiiRh7LMn3Se5vvDxdAKapw3WQGsh6jGNL1Xc5ZERy9va8nT7WAjKqY3g7ddgEaKBTjoZw/s1600/%25CE%2592%25CE%25A1%25CE%2591%25CE%2592%25CE%2595%25CE%2599%25CE%259F8.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="360" data-original-width="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCFv-VqiSYN_Zd0hesrZ_JvtzSrX2mj2wO6PrA1nLzjhGHxnyJLsXT7zIzMLkp_q5hCb-G1XiiRh7LMn3Se5vvDxdAKapw3WQGsh6jGNL1Xc5ZERy9va8nT7WAjKqY3g7ddgEaKBTjoZw/s1600/%25CE%2592%25CE%25A1%25CE%2591%25CE%2592%25CE%2595%25CE%2599%25CE%259F8.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="font-family: "Times New Roman"; font-size: medium; line-height: 16px;"><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Το δημαρχείο της Στοκχόλμης </span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"><b> </b>Το βραβείο απονέμεται στη συνέχεια σε επίσημη τελετή και πραγματοποιείται κάθε χρόνο στις<b> 10 Δεκεμβρίου</b>,η επέτειος του θανάτου του<b> Νόμπελ.</b></span><br />
<span style="font-family: "verdana" , sans-serif;"><b><br /></b></span><span style="font-family: "verdana" , sans-serif;"><b> "Το αποκορύφωμα της τελετής βραβείων Νόμπελ στη Στοκχόλμη είναι όταν κάθε βραβευμένος με βραβείο Νόμπελ κάνει βήματα προς τα εμπρός για να λάβει το βραβείο από τα χέρια της Αυτού Μεγαλειότητας του Βασιλιά της Σουηδίας.....</b></span><br />
<span style="font-family: "verdana" , sans-serif;"><b><br /></b></span><span style="font-family: "verdana" , sans-serif;"><b> Παρουσία του κόσμου,ο βραβευμένος με βραβείο Νόμπελ λαμβάνει τρία πράγματα:ένα δίπλωμα,ένα μετάλλιο και ένα δίπλωμα που αναγράφεται το αιτιολογικό της απονομής"</b></span><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> </b>Η επίσημη τελετή <b>Νόμπελ </b>πραγματοποιείται κάθε χρόνο στο δημαρχείο της <b>Στοκχόλμης.</b></span><br />
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<span style="color: red; font-family: "verdana" , sans-serif;"><b>Η ΕΠΙΤΡΟΠΗ ΝΟΜΠΕΛ ΓΙΑ ΤΗ ΦΥΣΙΚΗ</b></span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> </b>Η<b> Επιτροπή Νόμπελ </b>στη<b> Βασιλική Σουηδική Ακαδημία Επιστημών </b>είναι υπεύθυνη για την επιλογή των υποψηφίων από τα ονόματα που υποβάλλονται προς εξέταση από ειδικευμένο προσωπικό,που έχουν προσκληθεί από επίσημες επιστολές.</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2-DabVLkuSmSTm7jtGz6aMcXExZN1ZTlcqRJgiiTT8FRLsAMFZPEuXfsz-OIEIh7rbXn04ZO854nyITaqs6Wb4Fc4icjw6pN-7NrdcokxKWd4lRvUJ-IZr2GW4M9QppOR4SPOoJyt2zQ/s1600/%25CE%2592%25CE%25A1%25CE%2591%25CE%2592%25CE%2595%25CE%2599%25CE%259F7.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="536" data-original-width="800" height="428" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2-DabVLkuSmSTm7jtGz6aMcXExZN1ZTlcqRJgiiTT8FRLsAMFZPEuXfsz-OIEIh7rbXn04ZO854nyITaqs6Wb4Fc4icjw6pN-7NrdcokxKWd4lRvUJ-IZr2GW4M9QppOR4SPOoJyt2zQ/s640/%25CE%2592%25CE%25A1%25CE%2591%25CE%2592%25CE%2595%25CE%2599%25CE%259F7.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption"><b><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Τα μέλη της επιτροπής εκλέγονται για μια περίοδο 3 ετών μεταξύ των μελών της Ακαδημίας</span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Τα μέλη της επιτροπής εκλέγονται για μια περίοδο<b> 3 ετών</b> μεταξύ των μελών της <b>Ακαδημίας.</b>Κατά την αξιολόγηση των προσόντων των υποψηφίων,η <b>Επιτροπή</b> επικουρείται από ειδικά επιφορτισμένους τεχνικούς συμβούλους.</span></div>
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<span style="color: blue; font-family: "verdana" , sans-serif;"><b>Björn </b><strong style="text-align: start;">Jonson</strong></span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span style="color: blue;"> </span><span class="Apple-style-span" style="color: purple;">(Πρόεδρος)</span></b></span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span class="Apple-style-span" style="color: blue;">Lars Bergström</span><span class="Apple-style-span" style="color: purple;"> </span></b><span class="Apple-style-span" style="color: purple;"><b>(Γραμματέας)</b></span></span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span class="Apple-style-span" style="color: blue;">Lars Brink</span><span class="Apple-style-span" style="color: purple;"> </span></b><span class="Apple-style-span" style="color: purple;"><b>(Μέλος)</b></span></span></div>
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<span style="color: blue; font-family: "verdana" , sans-serif;"><b>Björn </b><strong style="text-align: start;">Johansson</strong></span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span class="Apple-style-span" style="color: purple;"> </span></b><span class="Apple-style-span" style="color: purple;"><b>(Μέλος)</b></span></span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span class="Apple-style-span" style="color: blue;">Anne L'Huillier</span><span class="Apple-style-span" style="color: purple;"> </span></b><span class="Apple-style-span" style="color: purple;"><b>(Μέλος)</b></span></span></div>
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<strong style="line-height: 15px; text-align: start;"><span style="color: blue; font-family: "verdana" , sans-serif;">Per Delsing</span></strong><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <span class="Apple-style-span" style="color: purple;"><b>(Μέλος)</b></span></span></div>
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<b style="color: red; font-family: verdana, sans-serif; line-height: 16px; text-align: justify;">ΒΑΣΙΛΙΚΗ ΣΟΥΗΔΙΚΗ ΑΚΑΔΗΜΙΑ ΕΠΙΣΤΗΜΩΝ</b></div>
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<span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif;"><b>Σχηματίστηκε 2 Ιούνη του 1739</b></span><br />
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<span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif;"><b>Έδρα Στοκχόλμη,Σουηδία</b></span><br />
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<span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif;"><b>Σύνθεση 1600 μέλη</b></span><br />
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<span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif;"><b>175 ξένα μέλη</b></span><br />
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<span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif;"><b>Πρόεδρος Svante Lindqvist</b></span><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b>Η <span style="color: blue;">Βασιλική Σουηδική Ακαδημία Επιστημών</span> είναι μία από τις βασιλικές ακαδημίες της Σουηδίας.</b>Η<b> Ακαδημία </b>είναι μια ανεξάρτητη,μη κυβερνητική επιστημονική οργάνωση που δρα για την προαγωγή των επιστημών,κυρίως στις φυσικές επιστήμες και τα μαθηματικά.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Η <b>Ακαδημία</b> ιδρύθηκε στις <b>2 Ιουνίου 1739 </b>από το φυσιοδίφη <b>Carl Linnaeus</b>,από το <b>Jonas Alströmer</b>,από το μηχανολόγο μηχανικό <b>Marten Triewald</b>,από τους δημόσιους υπάλληλους <b>Sten Carl Bielke</b> και <b>Carl Wilhelm Cederhielm</b>,και από το πολιτικό <b>Anders Johan von Höpken</b>.<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
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<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Η Βασιλική Σουηδική Ακαδημία Επιστημών</span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Ο σκοπός της <b>Ακαδημίας</b> είναι να επικεντρωθεί σε πρακτικές χρήσιμες γνώσεις,και να δημοσιεύσει στα σουηδικά,προκειμένου να διαδοθούν ευρέως τα πορίσματα της <b>Ακαδημίας</b>.Η <b>Ακαδημία </b>είχε ως στόχο να είναι διαφορετική από το <b>Royal Society of Sciences </b>στην <b>Ουψάλα</b>,το οποίο είχε ιδρυθεί το <b>1719</b> και δημοσίευε στα λατινικά.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Η τοποθεσία της είναι κοντά στην εμπορική δραστηριότητα στην πρωτεύουσα της <b>Σουηδίας</b> (η οποία σε αντίθεση με την<b> Ουψάλα</b> δεν έχει πανεπιστήμιο αυτή τη στιγμή).Η ακαδημία αυτή </span><span style="font-family: "verdana" , sans-serif;">διαμορφώθηκε με την βοήθεια της <b>Βασιλικής Εταιρείας</b> του<b> Λονδίνου</b> και της <b>Academie Royale des Sciences</b> του <b>Παρισιού,</b>στη<b> Γαλλία.</b></span><br />
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<span style="color: red; font-family: "verdana" , sans-serif;"><b>ΑΡΙΘΜΟΣ ΒΡΑΒΕΙΩΝ ΝΟΜΠΕΛ ΣΤΗ ΦΥΣΙΚΗ</b></span><br />
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<b style="font-family: verdana, sans-serif;"> 105 βραβεία Νόμπελ Φυσικής έχουν απονεμηθεί από το 1901.</b><span style="font-family: "verdana" , sans-serif;">Δεν έχουν απονεμηθεί έξι φορές:το </span><b style="font-family: verdana, sans-serif;">1916,1931,1934,1940,1941,</b><span style="font-family: "verdana" , sans-serif;">και </span><b style="font-family: verdana, sans-serif;">1942.</b></div>
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<tr><td class="tr-caption"><b style="font-family: verdana, sans-serif; line-height: 16px; text-align: justify;"><span style="color: purple; font-size: small;">105 βραβεία Νόμπελ Φυσικής έχουν απονεμηθεί από το 1901</span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">Γιατί τα<b> βραβεία Νόμπελ </b>δεν χορηγούνται σε εκείνες τις χρονιές;Στο καταστατικό του το<b> Ίδρυμα Νόμπελ </b>λέει: </span><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b>«Εάν κανένα από τα έργα υπό εξέταση βρίσκουν να έχουν σημασία όπως αναφέρονται στην πρώτη παράγραφο,το χρηματικό έπαθλο θα είναι διαθέσιμο έως το επόμενο έτος εάν,ακόμη και τότε,το βραβείο δεν μπορεί να δοθεί,το ποσό προστίθεται στα ταμεία του Ιδρύματος."</b></span><br />
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<span style="font-family: "verdana" , sans-serif;"><b> </b>Κατά τη διάρκεια του <b>Α</b> </span><span style="font-family: "verdana" , sans-serif;">και <b>Β </b></span><span style="font-family: "verdana" , sans-serif;"><b>Παγκοσμίου Πολέμου</b>,λιγότερα βραβεία </span><b style="font-family: verdana, sans-serif;">Νόμπελ </b><span style="font-family: "verdana" , sans-serif;">απονεμήθηκαν.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-weight: bold;">47 Β</span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-weight: bold;">ραβεία Νόμπελ </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b>Φυσικής </b>έχουν δοθεί σε ένα μόνο φυσικό.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-weight: bold;">29 Β</span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-weight: bold;">ραβεία </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-weight: bold;">Νόμπελ </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b>Φυσικής</b> </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">μοιράζονται δύο βραβευθέντες.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-weight: bold;">29 </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-weight: bold;">Β</span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-weight: bold;">ραβεία Νόμπελ </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-weight: bold;">Φυσικής</span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-weight: bold;"> </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">μοιράζονται</span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> από </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">κοινού από τρεις </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">βραβευθέντες</span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Γιατί συμβαίνει αυτό;Στο καταστατικό του το <b>Ίδρυμα Νόμπελ</b> λέει: </span><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b>"Ένα ποσοστό του βραβείου μπορεί να είναι εξίσου μεταξύ δύο έργων,καθένα από τα οποία θεωρείται ότι αξίζει ένα βραβείο.Εάν μια εργασία που ανταμείβεται έχει παραχθεί από δύο ή τρία άτομα,το βραβείο πρέπει να απονεμηθεί σε όλους από κοινού.Σε καμία περίπτωση δεν μπορεί το </b><b>ποσοστό του βραβείου</b><b> να επιμερίζεται σε περισσότερα από τρία άτομα."</b></span></div>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif; font-size: medium;"><b>ΝΟΜΠΕΛΙΣΤΕΣ ΦΥΣΙΚΟΙ</b></span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b style="line-height: 16px;"> </b><span style="line-height: 16px;">Το</span><b style="line-height: 16px;"> Βραβείο Νόμπελ Φυσικής</b><span style="line-height: 16px;"> απονεμήθηκε σε </span><b style="line-height: 16px;">192</b><span style="line-height: 16px;"> βραβευθέντες</span><b style="line-height: 16px;"> 1901-2011.</b></span><br />
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<tr><td class="tr-caption"><b style="font-family: verdana, sans-serif; line-height: 16px; text-align: justify;"><span style="color: purple; font-size: small;">Ο John Bardeen</span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><span style="line-height: 16px;"> Όμως ο</span><b style="line-height: 16px;"> John Bardeen</b><span style="line-height: 16px;"> έχει βραβευτεί δύο φορές και άρα υπάρχουν</span><b style="line-height: 16px;"> 191 </b><span style="line-height: 16px;">άτομα που έχουν απονεμηθεί το</span><b style="line-height: 16px;"> βραβείο Νόμπελ Φυσικής</b><span style="line-height: 16px;"> από το </span><b style="line-height: 16px;">1901.</b></span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span class="Apple-style-span" style="color: red;">Ο ΝΕΑΡΟΤΕΡΟΣ ΝΟΜΠΕΛΙΣΤΑΣ ΦΥΣΙΚΟΣ</span></b></span><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> </b></span><b style="font-family: Verdana, sans-serif;">Μέχρι σήμερα,ο νεότερος βραβευμένος με βραβείο Νόμπελ στη Φυσική είναι ο </b><b style="font-family: verdana, sans-serif;"><span style="color: blue;">Lawrence Bragg</span></b><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">.</span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="font-family: "Times New Roman"; font-size: 13px;"><span class="Apple-style-span" style="font-size: small;"><span style="font-family: "verdana" , sans-serif;"> </span><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif;">Ο Lawrence Bragg</span></span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Ο <b>Ουίλιαμ Λώρενς Μπραγκ (William Lawrence Bragg,31 Μαρτίου 1890–1 Ιουλίου 1971)</b> ήταν Βρετανός φυσικός που γεννήθηκε στην <b>Αυστραλία</b> και μοιράστηκε το<b> Βραβείο Νόμπελ Φυσικής </b>του <b>1915</b> με τον πατέρα του,τον <b>Ουίλιαμ Χένρι Μπραγκ,</b>όταν </span><b style="font-family: Verdana, sans-serif;">ο οποίος ήταν 25 χρονών</b><span style="font-family: "verdana" , sans-serif;">. </span></div>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>Ο ΜΕΓΑΛΥΤΕΡΟΣ ΣΕ ΗΛΙΚΙΑ ΝΟΜΠΕΛΙΣΤΑΣ </b></span><b style="color: red; font-family: Verdana, sans-serif;">ΦΥΣΙΚΟΣ</b><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="font-family: "Times New Roman"; font-size: 13px;"><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Ο<span class="Apple-style-span"> Raymond Davis Jr</span></span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> Ο μεγαλύτερος σε ηλικία βραβευμένος με βραβείο Νόμπελ στη Φυσική μέχρι σήμερα είναι </b></span><span style="font-family: "verdana" , sans-serif;"><b>ο <span style="color: blue;">Raymond Davis Jr</span></b></span><b style="font-family: verdana, sans-serif;">,ο οποίος ήταν 88 ετών όταν του απονεμήθηκε το βραβείο Νόμπελ Φυσικής το 2002.</b></div>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΓΥΝΑΙΚΕΣ ΝΟΜΠΕΛΙΣΤΕΣ ΦΥΣΙΚΗΣ</b></span><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> </b>Από τα<b> 191 άτομα </b>που απονεμήθηκε το<b> βραβείο Νόμπελ</b> στη<b> Φυσική</b>,μόνο δύο είναι γυναίκες.</span></div>
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<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="font-size: 13px;"><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">H Marie Curie</span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b>1903-</b></span><b style="font-family: verdana, sans-serif;"><span style="color: blue;">Marie Curie</span></b><b style="font-family: verdana, sans-serif;"><span class="Apple-style-span" style="color: blue; font-size: small;"> </span>(βραβευμένη επίσης το 1911 με το βραβείο Νόμπελ Χημείας.)</b></div>
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<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="font-family: Verdana, sans-serif; text-align: -webkit-auto;"><span class="Apple-style-span" style="color: purple; font-size: small;">H Μaria Goeppert-Mayer</span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b>1963-</b></span><span style="color: blue; font-family: "verdana" , sans-serif;"><b>Μaria Goeppert-Mayer</b></span><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span class="Apple-style-span" style="color: red;">ΠΟΛΛΑΠΛΟΙ ΝΟΜΠΕΛΙΣΤΕΣ ΦΥΣΙΚΟΙ</span></b></span><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> Ο <span style="color: blue;">John Bardeen</span> είναι το μόνο πρόσωπο που έχει λάβει το βραβείο Νόμπελ στη Φυσική δύο φορές.</b></span><br />
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<span style="line-height: 16px;"> </span><b style="line-height: 16px;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><span style="text-align: start;">Ο </span><span style="text-align: start;">Τζον Μπαρντίν</span><span style="text-align: start;"> (John Bardeen,23 Μαΐου 1908–30 Ιανουαρίου 1991) ήταν Αμερικανός φυσικός και ηλεκτρολόγος μηχανικός,ο μόνος άνθρωπος στην Ιστορία που τιμήθηκε δύο φορές με το Βραβείο Νόμπελ Φυσικής:το 1956 για το τρανζίστορ (μαζί με τους Σόκλεϋ και Μπράταιην) και το 1972 για τη θεωρία της υπεραγωγιμότητας (μαζί με τους Κούπερ και Σρίφερ,γι' αυτό και ονομάσθηκε Θεωρία BCS,από τα αρχικά τους)</span></span></b></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> Η <span style="color: blue;">Μαρία Κιουρί</span> τιμήθηκε με το βραβείο Νόμπελ δύο φορές,μία φορά στη Φυσική και στη Χημεία μια φορά.</b></span></div>
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<b style="font-family: verdana, sans-serif;"><span style="color: blue;">John Bardeen</span></b></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b>Νόμπελ Φυσικής 1956</b></span></div>
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<b style="font-family: verdana, sans-serif;"><span style="color: blue;">Marie Curie</span></b></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b>Νόμπελ Φυσικής 1903</b></span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b>Νόμπελ Χημείας 1911</b></span></div>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΜΕΤΑΘΑΝΑΤΙΑ ΒΡΑΒΕΙΑ ΝΟΜΠΕΛ ΣΤΗ ΦΥΣΙΚΗ </b></span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> Δεν έχει υπάρξει κανένα μεταθανάτιο βραβείο Νόμπελ στη Φυσική.</b>Από το <b>1974</b>,το καταστατικό του το <b>Ίδρυμα Νόμπελ</b> ορίζει ότι ένα βραβείο δεν μπορεί να απονεμηθεί μετά θάνατον,εκτός εάν ο θάνατος επήλθε μετά την ανακοίνωση του <b>βραβείου Νόμπελ.</b></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Πριν από το <b>1974</b>,το<b> βραβείο Νόμπελ </b>έχει απονεμηθεί μόνο μετά τον θάνατό του δύο φορές:Στον <b>Dag Hammarskjold (Βραβείο Νόμπελ Ειρήνης 1961)</b> και στον <b>Erik Axel Karlfeldt (Βραβείο Νόμπελ Λογοτεχνίας 1931).</b></span></div>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΟΙΚΟΓΕΝΕΙΕΣ ΝΟΜΠΕΛΙΣΤΕΣ ΦΥΣΙΚΗΣ</b></span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span class="Apple-style-span" style="color: red;">Παντρεμένα ζευγάρια:</span></b></span><br />
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<span style="font-family: "verdana" , sans-serif;"><b> Στη <span style="color: blue;">Marie Curie</span> και στον <span style="color: blue;">Pierre Curie </span></b></span><b style="font-family: verdana, sans-serif;">απονεμήθηκε το βραβείο Νόμπελ Φυσικής το 1903</b><span style="font-family: verdana, sans-serif;">.Η</span><b style="font-family: verdana, sans-serif;"> Μαρία Κιουρί</b><span style="font-family: verdana, sans-serif;"> τιμήθηκε με το βραβείο </span><b style="font-family: verdana, sans-serif;">Νόμπελ </b><span style="font-family: verdana, sans-serif;">για δεύτερη φορά το</span><b style="font-family: verdana, sans-serif;"> 1911</b><span style="font-family: verdana, sans-serif;">,αυτή τη φορά να λαμβάνει το βραβείο </span><b style="font-family: verdana, sans-serif;">Νόμπελ Χημείας.</b></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Μία από τις κόρες της<b> Μαρίας</b> και του <b>Πιέρ Κιουρί</b>,η <b>Irene Joliot-Curie</b>,τιμήθηκε με το βραβείο <b>Νόμπελ Χημείας</b> το <b>1935</b> μαζί με τον σύζυγό της <b>Frédéric Joliot.</b></span></div>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>Πατέρας και γιος:</b></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_zmzhvk3MmaAX2ovYGVwj3WfwlOyjTeMpNAEA2sjQNyDuyVN5jT86d9JvstnoC2kc6w93mETEgPWR6fX51WO17RZP9iN8AT1Ty5gq9Zua7puLx-rk4rzikDK5l_iIOIYHw7oukTQ-rrw/s1600/%25CE%2592%25CE%25A1%25CE%2591%25CE%2592%25CE%2595%25CE%2599%25CE%259F6.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="300" data-original-width="428" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_zmzhvk3MmaAX2ovYGVwj3WfwlOyjTeMpNAEA2sjQNyDuyVN5jT86d9JvstnoC2kc6w93mETEgPWR6fX51WO17RZP9iN8AT1Ty5gq9Zua7puLx-rk4rzikDK5l_iIOIYHw7oukTQ-rrw/s1600/%25CE%2592%25CE%25A1%25CE%2591%25CE%2592%25CE%2595%25CE%2599%25CE%259F6.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;"><b style="color: purple; font-family: verdana, sans-serif; text-align: justify;">O </b><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif; text-align: justify;"><b>Niels Bohr,1922 και </b></span><b style="color: purple; font-family: verdana, sans-serif; text-align: justify;">O </b><b style="color: purple; font-family: verdana, sans-serif; text-align: justify;">Aage Ν. Bohr,1975</b></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b>O<span class="Apple-style-span" style="color: blue;"> </span><span class="Apple-style-span" style="color: blue;">William Bragg </span>και <span class="Apple-style-span" style="color: blue;">Lawrence Bragg</span>,1915</b></span></div>
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<b style="font-family: Verdana, sans-serif;">O </b><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span class="Apple-style-span" style="color: blue;">Niels Bohr</span>,1922 και </b></span><b style="font-family: Verdana, sans-serif;">O </b><b style="font-family: Verdana, sans-serif;"><span class="Apple-style-span" style="color: blue;">Aage Ν. Bohr</span>,1975</b></div>
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<b style="font-family: Verdana, sans-serif;">O </b><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span class="Apple-style-span" style="color: blue;">Manne Siegbahn</span>,1924 και </b></span><b style="font-family: Verdana, sans-serif;">O </b><b style="font-family: Verdana, sans-serif;"><span class="Apple-style-span" style="color: blue;">Kai Μ. Siegbahn</span>,1981</b></div>
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<b style="font-family: Verdana, sans-serif;">O </b><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span class="Apple-style-span" style="color: blue;">JJ Thomson</span>,1906 και<span class="Apple-style-span" style="color: blue;"> </span></b></span><b style="font-family: Verdana, sans-serif;">O </b><b style="font-family: Verdana, sans-serif;"><span class="Apple-style-span" style="color: blue;">George Paget Thomson</span>,1937</b></div>
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<tr><td class="tr-caption"><b style="font-family: verdana, sans-serif; line-height: 16px; text-align: justify;"><span style="color: purple; font-size: small;">O William Bragg και Lawrence Bragg</span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> </b>Η λέξη <b>«Νόμπελ» </b>αναφέρεται στην ύπαρξη από το στεφάνι δάφνης.</span></div>
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<tr><td class="tr-caption"><span style="font-size: small;"><b style="color: purple; font-family: verdana, sans-serif;">O </b><b style="color: purple; font-family: verdana, sans-serif;">Kai Μ. Siegbahn</b></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Στην ελληνική μυθολογία,ο<b> θεός Απόλλων</b> απεικονίζεται φορώντας ένα δάφνινο στεφάνι στο κεφάλι του.</span><br />
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<tr><td class="tr-caption"><span style="font-size: small;"><b style="color: purple; font-family: verdana, sans-serif;">O </b><span class="Apple-style-span" style="color: purple; font-family: "verdana" , sans-serif;"><b>Manne Siegbahn</b></span></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Ένα στεφάνι δάφνης είναι ένα κυκλικό στεφάνι από κλαδιά και φύλλα της δάφνης (στα λατινικά:<b>Laurus nobilis</b>).</span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span class="Apple-style-span" style="color: purple; font-size: small;"><b style="font-family: Verdana, sans-serif; text-align: -webkit-auto;">O </b><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;"><b>JJ Thomson και </b></span><b style="font-family: Verdana, sans-serif; text-align: -webkit-auto;">O </b><b style="font-family: Verdana, sans-serif; text-align: -webkit-auto;">George Paget Thomson</b></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Στην<b> αρχαία Eλλάδα </b>στεφάνια δάφνης απονεμήθηκαν σε νικητές ως ένδειξη τιμής σε αθλητικές διοργανώσεις.</span></div>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif; font-size: medium;"><b>ΟΙ ΜΕΓΑΛΟΙ ΝΙΚΗΤΕΣ ΒΡΑΒΕΙΟΥ ΝΟΜΠΕΛ ΦΥΣΙΚΗΣ</b></span></div>
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<tr style="background: rgb(236, 236, 236);"><th><span style="color: red; font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Έτος</span></th><th colspan="2"><span style="color: blue; font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Όνομα</span></th><th><span style="color: purple; font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χώρα</span></th><th><span style="color: #274e13; font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Θέμα</span></th></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1901</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:WilhelmR%C3%B6ntgen.JPG" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="WilhelmRöntgen.JPG" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/WilhelmR%C3%B6ntgen.JPG/75px-WilhelmR%C3%B6ntgen.JPG" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/WilhelmR%C3%B6ntgen.JPG/113px-WilhelmR%C3%B6ntgen.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/WilhelmR%C3%B6ntgen.JPG/150px-WilhelmR%C3%B6ntgen.JPG 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Βίλχελμ Κόνραντ Ρέντγκεν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a class="image" href="https://commons.wikimedia.org/wiki/File:Flag_of_Prussia_(1892-1918).svg" style="background: none; color: #0b0080;"><img alt="Flag of Prussia (1892-1918).svg" data-file-height="901" data-file-width="1501" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Flag_of_Prussia_%281892-1918%29.svg/20px-Flag_of_Prussia_%281892-1918%29.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Flag_of_Prussia_%281892-1918%29.svg/30px-Flag_of_Prussia_%281892-1918%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Flag_of_Prussia_%281892-1918%29.svg/40px-Flag_of_Prussia_%281892-1918%29.svg.png 2x" style="border: 0px; vertical-align: middle;" width="20" /></a> Πρωσία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη των ακτίνων Χ»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1902</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Hendrik_Antoon_Lorentz.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Hendrik Antoon Lorentz.jpg" data-file-height="600" data-file-width="420" height="107" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hendrik_Antoon_Lorentz.jpg/75px-Hendrik_Antoon_Lorentz.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hendrik_Antoon_Lorentz.jpg/113px-Hendrik_Antoon_Lorentz.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hendrik_Antoon_Lorentz.jpg/150px-Hendrik_Antoon_Lorentz.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χέντρικ Αντόον Λόρεντζ</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9F%CE%BB%CE%BB%CE%B1%CE%BD%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ολλανδία"><img alt="Flag of the Netherlands.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/23px-Flag_of_the_Netherlands.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/35px-Flag_of_the_Netherlands.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/45px-Flag_of_the_Netherlands.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ολλανδία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις έρευνές τους πάνω στην επιρροή του μαγνητισμού σε φαινόμενα ακτινοβολίας» (Φαινόμενο Ζέεμαν)</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Pieter_Zeeman.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Pieter Zeeman.jpg" data-file-height="2974" data-file-width="2123" height="105" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Pieter_Zeeman.jpg/75px-Pieter_Zeeman.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Pieter_Zeeman.jpg/113px-Pieter_Zeeman.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Pieter_Zeeman.jpg/150px-Pieter_Zeeman.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πιέτερ Ζέεμαν</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1903</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Becquerel_Henri_photograph.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Becquerel Henri photograph.jpg" data-file-height="344" data-file-width="261" height="99" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/70/Becquerel_Henri_photograph.jpg/75px-Becquerel_Henri_photograph.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Becquerel_Henri_photograph.jpg/113px-Becquerel_Henri_photograph.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Becquerel_Henri_photograph.jpg/150px-Becquerel_Henri_photograph.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ανρί Μπεκερέλ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της αυθόρμητης ραδιενέργειας»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:PierreCurie.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="PierreCurie.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9c/PierreCurie.jpg/75px-PierreCurie.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/PierreCurie.jpg/113px-PierreCurie.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/PierreCurie.jpg/150px-PierreCurie.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πιερ Κιουρί</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις έρευνές τους πάνω στα φαινόμενα ακτινοβολίας που ανακάλυψε ο Ανρί Μπεκερέλ»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Mariecurie.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Mariecurie.jpg" data-file-height="1987" data-file-width="1536" height="97" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Mariecurie.jpg/75px-Mariecurie.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Mariecurie.jpg/113px-Mariecurie.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Mariecurie.jpg/150px-Mariecurie.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μαρία Κιουρί</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%BF%CE%BB%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Πολωνία"><img alt="Flag of Poland.svg" class="thumbborder" data-file-height="400" data-file-width="640" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/12/Flag_of_Poland.svg/23px-Flag_of_Poland.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Flag_of_Poland.svg/35px-Flag_of_Poland.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/12/Flag_of_Poland.svg/46px-Flag_of_Poland.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Πολωνία</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1904</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:John_William_Strutt.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="John William Strutt.jpg" data-file-height="1077" data-file-width="800" height="101" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/28/John_William_Strutt.jpg/75px-John_William_Strutt.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/John_William_Strutt.jpg/113px-John_William_Strutt.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/John_William_Strutt.jpg/150px-John_William_Strutt.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζον Ουίλιαμ Στρατ, 3ος Βαρώνος Ράλεϊ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;">«για τις έρευνές του πάνω στις πυκνότητες των πιο σημαντικών αερίων και για την ανακάλυψη του αργού σε συσχέτιση με τις παραπάνω μελέτε</span>»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1905</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Phillipp_Lenard_in_1900.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Phillipp Lenard in 1900.jpg" data-file-height="450" data-file-width="338" height="100" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Phillipp_Lenard_in_1900.jpg/75px-Phillipp_Lenard_in_1900.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Phillipp_Lenard_in_1900.jpg/113px-Phillipp_Lenard_in_1900.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Phillipp_Lenard_in_1900.jpg/150px-Phillipp_Lenard_in_1900.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Φίλιπ Έντουαρντ Άντον φον Λέναρντ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις εργασίες του επί των καθοδικών ακτίνων»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1906</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Jj-thomson3.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Jj-thomson3.jpg" data-file-height="780" data-file-width="624" height="94" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Jj-thomson3.jpg/75px-Jj-thomson3.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Jj-thomson3.jpg/113px-Jj-thomson3.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Jj-thomson3.jpg/150px-Jj-thomson3.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σερ Τζόζεφ Τζον Τόμσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«ως αναγνώριση για τη συμβολή του στις θεωρητικές και πειραματικές εργασίες επί της ηλεκτρικής αγωγιμότητας των αερίων»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1907</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Albert_Abraham_Michelson2.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Albert Abraham Michelson2.jpg" data-file-height="1286" data-file-width="916" height="105" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Albert_Abraham_Michelson2.jpg/75px-Albert_Abraham_Michelson2.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Albert_Abraham_Michelson2.jpg/113px-Albert_Abraham_Michelson2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Albert_Abraham_Michelson2.jpg/150px-Albert_Abraham_Michelson2.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Άλμπερτ Έιμπραχαμ Μάικελσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις οπτικές συσκευές ακριβείας (που κατασκεύασε) και τις εργασίες στη Φασματοσκοπία που ακολούθησαν με τη βοήθειά τους». Βλ. και Πείραμα Μάικελσον-Μόρλεϋ</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1908</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:G_lippmann.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="G lippmann.jpg" data-file-height="263" data-file-width="200" height="99" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/bf/G_lippmann.jpg/75px-G_lippmann.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/G_lippmann.jpg/113px-G_lippmann.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/G_lippmann.jpg/150px-G_lippmann.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γκάμπριελ Λίπμαν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%BF%CF%85%CE%BE%CE%B5%CE%BC%CE%B2%CE%BF%CF%8D%CF%81%CE%B3%CE%BF" style="background: none; color: #0b0080;" title="Λουξεμβούργο"><img alt="Flag of Luxembourg.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/da/Flag_of_Luxembourg.svg/23px-Flag_of_Luxembourg.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Flag_of_Luxembourg.svg/35px-Flag_of_Luxembourg.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/Flag_of_Luxembourg.svg/46px-Flag_of_Luxembourg.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Λουξεμβούργο</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη μέθοδο της αναπαραγωγής χρωμάτων φωτογραφικά, βασισμένη στο φαινόμενο της συμβολής»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1909</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Guglielmo_Marconi.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Guglielmo Marconi.jpg" data-file-height="1314" data-file-width="987" height="100" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Guglielmo_Marconi.jpg/75px-Guglielmo_Marconi.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Guglielmo_Marconi.jpg/113px-Guglielmo_Marconi.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Guglielmo_Marconi.jpg/150px-Guglielmo_Marconi.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γκουλιέλμο Μαρκόνι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CF%84%CE%B1%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιταλία"><img alt="Flag of Italy.svg" class="thumbborder" data-file-height="1000" data-file-width="1500" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/23px-Flag_of_Italy.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/35px-Flag_of_Italy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/45px-Flag_of_Italy.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιταλία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή τους στην ανάπτυξη της ασύρματης τηλεγραφίας»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Ferdinand_Braun.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Ferdinand Braun.jpg" data-file-height="1024" data-file-width="747" height="103" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/55/Ferdinand_Braun.jpg/75px-Ferdinand_Braun.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Ferdinand_Braun.jpg/113px-Ferdinand_Braun.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Ferdinand_Braun.jpg/150px-Ferdinand_Braun.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Καρλ Φέρντιναντ Μπράουν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1910</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Johannes_Diderik_van_der_Waals.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Johannes Diderik van der Waals.jpg" data-file-height="1131" data-file-width="1000" height="85" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Johannes_Diderik_van_der_Waals.jpg/75px-Johannes_Diderik_van_der_Waals.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Johannes_Diderik_van_der_Waals.jpg/113px-Johannes_Diderik_van_der_Waals.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Johannes_Diderik_van_der_Waals.jpg/150px-Johannes_Diderik_van_der_Waals.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γιοχάνες Ντίντερικ Βαν Ντερ Βάαλς</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9F%CE%BB%CE%BB%CE%B1%CE%BD%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ολλανδία"><img alt="Flag of the Netherlands.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/23px-Flag_of_the_Netherlands.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/35px-Flag_of_the_Netherlands.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/45px-Flag_of_the_Netherlands.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ολλανδία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εργασία του στην καταστατική εξίσωση για τα αέρια και τα υγρά»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1911</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Wilhelm_Wien_1911.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Wilhelm Wien 1911.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Wilhelm_Wien_1911.jpg/75px-Wilhelm_Wien_1911.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Wilhelm_Wien_1911.jpg/113px-Wilhelm_Wien_1911.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Wilhelm_Wien_1911.jpg/150px-Wilhelm_Wien_1911.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Βίλχελμ Βιν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις ανακαλύψεις του πάνω στους νόμους που διέπουν τη θερμική ακτινοβολία» </span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1912</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Nils_Gustaf_Dal%C3%A9n.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Nils Gustaf Dalén.jpg" data-file-height="1312" data-file-width="869" height="113" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/56/Nils_Gustaf_Dal%C3%A9n.jpg/75px-Nils_Gustaf_Dal%C3%A9n.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Nils_Gustaf_Dal%C3%A9n.jpg/113px-Nils_Gustaf_Dal%C3%A9n.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/Nils_Gustaf_Dal%C3%A9n.jpg/150px-Nils_Gustaf_Dal%C3%A9n.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Νιλς Γκούσταφ Νταλέν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A3%CE%BF%CF%85%CE%B7%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Σουηδία"><img alt="Flag of Sweden.svg" class="thumbborder" data-file-height="1000" data-file-width="1600" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/23px-Flag_of_Sweden.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/35px-Flag_of_Sweden.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/46px-Flag_of_Sweden.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Σουηδία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εφεύρεση των αυτόματων ρυθμιστών για το φωτισμό σε φάρους και σημαδούρες»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1913</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Kamerlingh_portret.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Kamerlingh portret.jpg" data-file-height="800" data-file-width="600" height="100" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/94/Kamerlingh_portret.jpg/75px-Kamerlingh_portret.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Kamerlingh_portret.jpg/113px-Kamerlingh_portret.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/Kamerlingh_portret.jpg/150px-Kamerlingh_portret.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χάικε Κάμερλιν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9F%CE%BB%CE%BB%CE%B1%CE%BD%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ολλανδία"><img alt="Flag of the Netherlands.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/23px-Flag_of_the_Netherlands.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/35px-Flag_of_the_Netherlands.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/45px-Flag_of_the_Netherlands.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ολλανδία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις έρευνες στις ιδιότητες της ύλης σε χαμηλές θερμοκρασίες, οι οποίες οδήγησαν στην παραγωγή του υγρού ήλιου»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1914</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Max_von_Laue.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Max von Laue.jpg" data-file-height="2539" data-file-width="1795" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Max_von_Laue.jpg/75px-Max_von_Laue.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Max_von_Laue.jpg/113px-Max_von_Laue.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Max_von_Laue.jpg/150px-Max_von_Laue.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μαξ φον Λάουε</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της σκέδασης των ακτίνων Χ από κρυστάλλους»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1915</span></td><td><div class="floatleft" style="clear: left; float: left; margin: 0px 0.5em 0.5em 0px; position: relative;">
<a class="image" href="https://commons.wikimedia.org/wiki/File:William_Henry_Bragg_Nobel.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="William Henry Bragg" data-file-height="2271" data-file-width="1480" height="118" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/21/William_Henry_Bragg_Nobel.jpg/77px-William_Henry_Bragg_Nobel.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/William_Henry_Bragg_Nobel.jpg/115px-William_Henry_Bragg_Nobel.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/William_Henry_Bragg_Nobel.jpg/154px-William_Henry_Bragg_Nobel.jpg 2x" style="border: 0px; vertical-align: middle;" width="77" /></span></a></div>
</td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σερ Γουίλιαμ Χένρι Μπραγκ</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή τους στην ανάλυση της κρυσταλλικής δομής με ακτίνες Χ»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Wl-bragg.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Wl-bragg.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Wl-bragg.jpg/75px-Wl-bragg.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Wl-bragg.jpg/113px-Wl-bragg.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Wl-bragg.jpg/150px-Wl-bragg.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γουίλιαμ Λόρενς Μπραγκ</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1916</span></td><td colspan="4" style="text-align: center;"><i><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Δεν δόθηκε</span></i></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1917</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Charles_Glover_Barkla.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Charles Glover Barkla.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/81/Charles_Glover_Barkla.jpg/75px-Charles_Glover_Barkla.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Charles_Glover_Barkla.jpg/113px-Charles_Glover_Barkla.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Charles_Glover_Barkla.jpg/150px-Charles_Glover_Barkla.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τσαρλς Γκλόβερ Μπάρκλα</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της χαρακτηριστικής ακτινοβολίας Ρέντγκεν των στοιχείων»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1918</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Max_Planck_(Nobel_1918).jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Max Planck (Nobel 1918).jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/42/Max_Planck_%28Nobel_1918%29.jpg/75px-Max_Planck_%28Nobel_1918%29.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Max_Planck_%28Nobel_1918%29.jpg/113px-Max_Planck_%28Nobel_1918%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Max_Planck_%28Nobel_1918%29.jpg/150px-Max_Planck_%28Nobel_1918%29.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μαξ Πλανκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«ως αναγνώριση για τη συμβολή του στην εξέλιξη της φυσικής με την ανακάλυψη των κβάντων ενέργειας»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1919</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Johannes_Stark.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Johannes Stark.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Johannes_Stark.jpg/75px-Johannes_Stark.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Johannes_Stark.jpg/113px-Johannes_Stark.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Johannes_Stark.jpg/150px-Johannes_Stark.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γιοχάννες Σταρκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη του φαινομένου Ντόπλερ»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1920</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Guillaume_1920.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Guillaume 1920.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Guillaume_1920.jpg/75px-Guillaume_1920.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Guillaume_1920.jpg/113px-Guillaume_1920.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Guillaume_1920.jpg/150px-Guillaume_1920.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σαρλ Εντουάρ Γκιγιόμ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BB%CE%B2%CE%B5%CF%84%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ελβετία"><img alt="Flag of Switzerland.svg" class="thumbborder" data-file-height="1000" data-file-width="1000" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/15px-Flag_of_Switzerland.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/23px-Flag_of_Switzerland.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/30px-Flag_of_Switzerland.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="15" /></a> Ελβετία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή του σε πειράματα ακριβείας, μέσω της ανακάλυψης ανωμαλιών στα κράματα νικελίου - ατσαλιού»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1921</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Einstein1921_by_F_Schmutzer_4.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Einstein1921 by F Schmutzer 4.jpg" data-file-height="1475" data-file-width="1182" height="94" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/78/Einstein1921_by_F_Schmutzer_4.jpg/75px-Einstein1921_by_F_Schmutzer_4.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Einstein1921_by_F_Schmutzer_4.jpg/113px-Einstein1921_by_F_Schmutzer_4.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/Einstein1921_by_F_Schmutzer_4.jpg/150px-Einstein1921_by_F_Schmutzer_4.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Άλμπερτ Αινστάιν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή του στη θεωρητική φυσική, και για την εξήγηση του φωτοηλεκτρικού φαινομένου»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1922</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Niels_Bohr.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Niels Bohr.jpg" data-file-height="2048" data-file-width="1456" height="105" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Niels_Bohr.jpg/75px-Niels_Bohr.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Niels_Bohr.jpg/113px-Niels_Bohr.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Niels_Bohr.jpg/150px-Niels_Bohr.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Νιλς Χένρικ Ντάβιντ Μπορ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Δανία"><img alt="Flag of Denmark.svg" class="thumbborder" data-file-height="560" data-file-width="740" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Flag_of_Denmark.svg/20px-Flag_of_Denmark.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Flag_of_Denmark.svg/31px-Flag_of_Denmark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Flag_of_Denmark.svg/40px-Flag_of_Denmark.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="20" /></a> Δανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την έρευνά του επί της δομής των ατόμων και της ακτινοβολίας που προέρχεται από αυτά»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1923</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Robert-millikan2.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Robert-millikan2.jpg" data-file-height="237" data-file-width="180" height="99" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Robert-millikan2.jpg/75px-Robert-millikan2.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Robert-millikan2.jpg/113px-Robert-millikan2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Robert-millikan2.jpg/150px-Robert-millikan2.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ρόμπερτ Άντριους Μίλλικαν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εργασία του πάνω στο στοιχειώδες φορτίο του ηλεκτρικού ρεύματος και στο φωτοηλεκτρικό φαινόμενο»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1924</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:1924_Karl_Manne_Siegbahn.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="1924 Karl Manne Siegbahn.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/eb/1924_Karl_Manne_Siegbahn.jpg/75px-1924_Karl_Manne_Siegbahn.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/1924_Karl_Manne_Siegbahn.jpg/113px-1924_Karl_Manne_Siegbahn.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/1924_Karl_Manne_Siegbahn.jpg/150px-1924_Karl_Manne_Siegbahn.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Καρλ Σίγκμπαν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A3%CE%BF%CF%85%CE%B7%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Σουηδία"><img alt="Flag of Sweden.svg" class="thumbborder" data-file-height="1000" data-file-width="1600" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/23px-Flag_of_Sweden.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/35px-Flag_of_Sweden.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/46px-Flag_of_Sweden.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Σουηδία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εργασία του πάνω στη στερεοσκοπία ακτίνων Χ»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1925</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:James_Franck.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="James Franck.jpg" data-file-height="300" data-file-width="378" height="60" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/James_Franck.jpg/75px-James_Franck.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/James_Franck.jpg/113px-James_Franck.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/James_Franck.jpg/150px-James_Franck.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζέημς Φρανκ</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη των νόμων που διέπουν την κρούση ενός ηλεκτρονίου με ένα άτομο»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Gustav_Hertz.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Gustav Hertz.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Gustav_Hertz.jpg/75px-Gustav_Hertz.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Gustav_Hertz.jpg/113px-Gustav_Hertz.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Gustav_Hertz.jpg/150px-Gustav_Hertz.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γκούσταφ Χερτς</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1926</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Jean_Perrin_1926.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Jean Perrin 1926.jpg" data-file-height="1074" data-file-width="816" height="99" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Jean_Perrin_1926.jpg/75px-Jean_Perrin_1926.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Jean_Perrin_1926.jpg/113px-Jean_Perrin_1926.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Jean_Perrin_1926.jpg/150px-Jean_Perrin_1926.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ζαν Μπατίστ Περέν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εργασία του επί της ασυνεχούς δομής της ύλης»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1927</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Arthur_Holly_Compton.gif" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Arthur Holly Compton.gif" data-file-height="174" data-file-width="237" height="55" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/85/Arthur_Holly_Compton.gif/75px-Arthur_Holly_Compton.gif" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Arthur_Holly_Compton.gif/113px-Arthur_Holly_Compton.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Arthur_Holly_Compton.gif/150px-Arthur_Holly_Compton.gif 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Άρθουρ Χόλι Κόμπτον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη του φαινομένου που πήρε το όνομά του, βλ. Φαινόμενο Κόμπτον»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Charles_Thomson_Rees_Wilson_at_1927_Solvay_conference.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Charles Thomson Rees Wilson at 1927 Solvay conference.jpg" data-file-height="202" data-file-width="189" height="80" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/37/Charles_Thomson_Rees_Wilson_at_1927_Solvay_conference.jpg/75px-Charles_Thomson_Rees_Wilson_at_1927_Solvay_conference.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Charles_Thomson_Rees_Wilson_at_1927_Solvay_conference.jpg/113px-Charles_Thomson_Rees_Wilson_at_1927_Solvay_conference.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/Charles_Thomson_Rees_Wilson_at_1927_Solvay_conference.jpg/150px-Charles_Thomson_Rees_Wilson_at_1927_Solvay_conference.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τσαρλς Τόμσον Ρις Γουίλσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Σκωτία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη μέθοδο που κάνει ορατές τις τροχιές φορτισμένων σωματιδίων, μέσω υγροποίησης σταγονιδίων»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1928</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Niels_BohrUpOwenWillansRichardsonDownSolvay1927.JPG" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Niels BohrUpOwenWillansRichardsonDownSolvay1927.JPG" data-file-height="891" data-file-width="424" height="158" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Niels_BohrUpOwenWillansRichardsonDownSolvay1927.JPG/75px-Niels_BohrUpOwenWillansRichardsonDownSolvay1927.JPG" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Niels_BohrUpOwenWillansRichardsonDownSolvay1927.JPG/113px-Niels_BohrUpOwenWillansRichardsonDownSolvay1927.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Niels_BohrUpOwenWillansRichardsonDownSolvay1927.JPG/150px-Niels_BohrUpOwenWillansRichardsonDownSolvay1927.JPG 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Όουεν Γουίλανς Ρίτσαρντσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εργασία του στο θερμιονικό φαινόμενο και ειδικότερα για την ανακάλυψη του νόμου που πήρε το όνομά του»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1929</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Broglie_Big.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Broglie Big.jpg" data-file-height="381" data-file-width="300" height="95" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Broglie_Big.jpg/75px-Broglie_Big.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Broglie_Big.jpg/113px-Broglie_Big.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Broglie_Big.jpg/150px-Broglie_Big.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πρίγκηπας Λουί-Βικτόρ Πιερ Ραϋμόν, Δούκας του Μπρολί</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της κυματικής φύσης των ηλεκτρονίων»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1930</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Sir_CV_Raman.JPG" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Sir CV Raman.JPG" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Sir_CV_Raman.JPG/75px-Sir_CV_Raman.JPG" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Sir_CV_Raman.JPG/113px-Sir_CV_Raman.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Sir_CV_Raman.JPG/150px-Sir_CV_Raman.JPG 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τσαντρασεχάρα Βενκάτα Ραμάν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%BD%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ινδία"><img alt="Flag of India.svg" class="thumbborder" data-file-height="900" data-file-width="1350" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_India.svg/23px-Flag_of_India.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_India.svg/35px-Flag_of_India.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_India.svg/45px-Flag_of_India.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ινδία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εργασία του στη διάχυση του φωτός και την ανακάλυψη του φαινομένου που φέρει το όνομά του»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1931</span></td><td colspan="4" style="text-align: center;"><i><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Δεν απονεμήθηκε</span></i></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1932</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Werner_Heisenberg_at_1927_Solvay_Conference.JPG" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Werner Heisenberg at 1927 Solvay Conference.JPG" data-file-height="840" data-file-width="630" height="100" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Werner_Heisenberg_at_1927_Solvay_Conference.JPG/75px-Werner_Heisenberg_at_1927_Solvay_Conference.JPG" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Werner_Heisenberg_at_1927_Solvay_Conference.JPG/113px-Werner_Heisenberg_at_1927_Solvay_Conference.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Werner_Heisenberg_at_1927_Solvay_Conference.JPG/150px-Werner_Heisenberg_at_1927_Solvay_Conference.JPG 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Βέρνερ Καρλ Χάιζενμπεργκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη δημιουργία της Κβαντομηχανικής»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1933</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Erwin_Schr%C3%B6dinger_(1933).jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Erwin Schrödinger (1933).jpg" data-file-height="900" data-file-width="652" height="108" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Erwin_Schr%C3%B6dinger_%281933%29.jpg/78px-Erwin_Schr%C3%B6dinger_%281933%29.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Erwin_Schr%C3%B6dinger_%281933%29.jpg/117px-Erwin_Schr%C3%B6dinger_%281933%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Erwin_Schr%C3%B6dinger_%281933%29.jpg/156px-Erwin_Schr%C3%B6dinger_%281933%29.jpg 2x" style="border: 0px; vertical-align: middle;" width="78" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Έρβιν Σρέντιγκερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%85%CF%83%CF%84%CF%81%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Αυστρία"><img alt="Flag of Austria.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_Austria.svg/23px-Flag_of_Austria.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_Austria.svg/35px-Flag_of_Austria.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_Austria.svg/45px-Flag_of_Austria.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αυστρία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη νέων, παραγωγικών μορφών της ατομικής θεωρίας»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Dirac_4.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Dirac 4.jpg" data-file-height="1107" data-file-width="750" height="111" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Dirac_4.jpg/75px-Dirac_4.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Dirac_4.jpg/113px-Dirac_4.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Dirac_4.jpg/150px-Dirac_4.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πολ Άντριεν Μορίς Ντιράκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1934</span></td><td colspan="4" style="text-align: center;"><i><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Δεν δόθηκε</span></i></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1935</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:James_Chadwick.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="James Chadwick.jpg" data-file-height="1650" data-file-width="1320" height="94" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/James_Chadwick.jpg/75px-James_Chadwick.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/James_Chadwick.jpg/113px-James_Chadwick.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/James_Chadwick.jpg/150px-James_Chadwick.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζέιμς Τσάντγουικ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη του νετρονίου»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1936</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Hess.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Hess.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Hess.jpg/75px-Hess.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Hess.jpg/113px-Hess.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Hess.jpg/150px-Hess.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Βίκτορ Φραντς Ες</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%85%CF%83%CF%84%CF%81%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Αυστρία"><img alt="Flag of Austria.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_Austria.svg/23px-Flag_of_Austria.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_Austria.svg/35px-Flag_of_Austria.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_Austria.svg/45px-Flag_of_Austria.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αυστρία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της κοσμικής ακτινοβολίας»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Carl_anderson.1937.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Carl anderson.1937.jpg" data-file-height="414" data-file-width="250" height="124" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Carl_anderson.1937.jpg/75px-Carl_anderson.1937.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Carl_anderson.1937.jpg/113px-Carl_anderson.1937.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Carl_anderson.1937.jpg/150px-Carl_anderson.1937.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Καρλ Ντέιβιντ Άντερσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη του ποζιτρονίου»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1937</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Clinton_Davisson.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Clinton Davisson.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/00/Clinton_Davisson.jpg/75px-Clinton_Davisson.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Clinton_Davisson.jpg/113px-Clinton_Davisson.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Clinton_Davisson.jpg/150px-Clinton_Davisson.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Κλίντον Τζόζεφ Ντέιβισον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την πειραματική ανακάλυψη της σκέδασης ηλεκτρονίων από κρυστάλλους»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:George_Paget_Thomson.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="George Paget Thomson.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c2/George_Paget_Thomson.jpg/75px-George_Paget_Thomson.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/George_Paget_Thomson.jpg/113px-George_Paget_Thomson.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/George_Paget_Thomson.jpg/150px-George_Paget_Thomson.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζορτζ Τόμσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1938</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Enrico_Fermi_1943-49.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Enrico Fermi 1943-49.jpg" data-file-height="2922" data-file-width="2358" height="93" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Enrico_Fermi_1943-49.jpg/75px-Enrico_Fermi_1943-49.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Enrico_Fermi_1943-49.jpg/113px-Enrico_Fermi_1943-49.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Enrico_Fermi_1943-49.jpg/150px-Enrico_Fermi_1943-49.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ενρίκο Φέρμι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CF%84%CE%B1%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιταλία"><img alt="Flag of Italy.svg" class="thumbborder" data-file-height="1000" data-file-width="1500" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/23px-Flag_of_Italy.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/35px-Flag_of_Italy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/45px-Flag_of_Italy.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιταλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την απόδειξη ύπαρξης καινούριων ραδιενεργών στοιχείων παραγόμενων με εκπομπή νετρονίου και για τη σχετική ανακάλυψη πυρηνικών αντιδράσεων προκαλούμενων από αργά νετρόνια»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1939</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Ernest_Orlando_Lawrence.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Ernest Orlando Lawrence.jpg" data-file-height="277" data-file-width="200" height="104" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/88/Ernest_Orlando_Lawrence.jpg/75px-Ernest_Orlando_Lawrence.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Ernest_Orlando_Lawrence.jpg/113px-Ernest_Orlando_Lawrence.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Ernest_Orlando_Lawrence.jpg/150px-Ernest_Orlando_Lawrence.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Έρνεστ Ορλάντο Λόρενς</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εφεύρεση και την εξέλιξη του κυκλότρου και για τα αποτελέσματα που αποκτήθηκαν μέσω αυτού, κυρίως αυτά που αφορούν τεχνητά ραδιενεργά στοιχεία»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1940</span></td><td colspan="4" style="text-align: center;"><i><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Δεν δόθηκε</span></i></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1941</span></td><td colspan="4" style="text-align: center;"><i><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Δεν δόθηκε</span></i></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1942</span></td><td colspan="4" style="text-align: center;"><i><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Δεν δόθηκε</span></i></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1943</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Otto_Stern.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Otto Stern.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/88/Otto_Stern.jpg/75px-Otto_Stern.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Otto_Stern.jpg/113px-Otto_Stern.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Otto_Stern.jpg/150px-Otto_Stern.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Όττο Στερν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή του στην ανάπτυξη της μεθόδου των μοριακών ακτίνων».</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1944</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Isidor_Isaac_Rabi.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Isidor Isaac Rabi.jpg" data-file-height="269" data-file-width="200" height="101" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/Isidor_Isaac_Rabi.jpg/75px-Isidor_Isaac_Rabi.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Isidor_Isaac_Rabi.jpg/113px-Isidor_Isaac_Rabi.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Isidor_Isaac_Rabi.jpg/150px-Isidor_Isaac_Rabi.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ίσιντορ Ισαάκ Ράμπι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη μέθοδο καταγραφής των μαγνητικών ιδιοτήτων του ατομικού πυρήνα».</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1945</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Wolfgang_Pauli_young.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Wolfgang Pauli young.jpg" data-file-height="300" data-file-width="250" height="90" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/43/Wolfgang_Pauli_young.jpg/75px-Wolfgang_Pauli_young.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Wolfgang_Pauli_young.jpg/113px-Wolfgang_Pauli_young.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/43/Wolfgang_Pauli_young.jpg/150px-Wolfgang_Pauli_young.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Βόλφγκανγκ Πάουλι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%85%CF%83%CF%84%CF%81%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Αυστρία"><img alt="Flag of Austria.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_Austria.svg/23px-Flag_of_Austria.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_Austria.svg/35px-Flag_of_Austria.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_Austria.svg/45px-Flag_of_Austria.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αυστρία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της Απαγορευτικής Αρχής» που φέρει το όνομά του.</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1946</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Bridgman.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Bridgman.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Bridgman.jpg/75px-Bridgman.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Bridgman.jpg/113px-Bridgman.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Bridgman.jpg/150px-Bridgman.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πέρσι Γουίλλιαμς Μπρίντγκμαν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εφεύρεση μιας συσκευής ικανής να παράγει εξαιρετικά υψηλές πιέσεις και για τις ανακαλύψεις που έκανε στο πεδίο της Φυσικής υψηλών πιέσεων»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1947</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:EVAppleton.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="EVAppleton.jpg" data-file-height="107" data-file-width="107" height="75" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/EVAppleton.jpg/75px-EVAppleton.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/6/6c/EVAppleton.jpg 1.5x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Έντουαρντ Βίκτορ Άπλετον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις έρευνές του στη Φυσική της ατμόσφαιρας, και για την ανακάλυψη του λεγόμενου στρώματος Άπλετον»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1948</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Blackett-large.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Blackett-large.jpg" data-file-height="194" data-file-width="133" height="109" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Blackett-large.jpg/75px-Blackett-large.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Blackett-large.jpg/113px-Blackett-large.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/c3/Blackett-large.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πάτρικ Μέιναρντ Στιούαρτ Μπλάκετ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εξέλιξη της μεθόδου του θαλάμου Γουίλσον (cloud chamber) και για τις ανακαλύψεις στην Πυρηνική Φυσική και την κοσμική ακτινοβολία»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1949</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Yukawa.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Yukawa.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Yukawa.jpg/75px-Yukawa.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Yukawa.jpg/113px-Yukawa.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Yukawa.jpg/150px-Yukawa.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χιντέκι Γιουκάουα</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B1%CF%80%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιαπωνία"><img alt="Flag of Japan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/23px-Flag_of_Japan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/35px-Flag_of_Japan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/45px-Flag_of_Japan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιαπωνία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την πρόβλεψη της ύπαρξης των μεσονίων, βασισμένη σε θεωρητική εργασία επί των πυρηνικών δυνάμεων»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1950</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Cecil_Powell.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Cecil Powell.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Cecil_Powell.jpg/75px-Cecil_Powell.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Cecil_Powell.jpg/113px-Cecil_Powell.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Cecil_Powell.jpg/150px-Cecil_Powell.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σέσιλ Φρανκ Πάουελ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανάπτυξη της φωτογραφικής μεθόδου μελέτης πυρηνικών διεργασιών και για τις ανακαλύψεις σχετικά με μεσόνια που έγιναν με αυτή τη μέθοδο»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1951</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζον Ντάγκλας Κόκροφτ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την πρωτότυπη εργασία τους πάνω στη μετατροπή του ατομικού πηρήνα, με τεχνητώς επιταχυνθέντα ατομικά σωματίδια»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Ernest_Walton.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Ernest Walton.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/65/Ernest_Walton.jpg/75px-Ernest_Walton.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Ernest_Walton.jpg/113px-Ernest_Walton.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Ernest_Walton.jpg/150px-Ernest_Walton.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Έρνεστ Τόμας Σάιντον Γουόλτον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CF%81%CE%BB%CE%B1%CE%BD%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιρλανδία"><img alt="Flag of Ireland.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/45/Flag_of_Ireland.svg/23px-Flag_of_Ireland.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Flag_of_Ireland.svg/35px-Flag_of_Ireland.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/45/Flag_of_Ireland.svg/46px-Flag_of_Ireland.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιρλανδία</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1952</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Felix_Bloch,_Stanford_University.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Felix Bloch, Stanford University.jpg" data-file-height="250" data-file-width="200" height="94" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Felix_Bloch%2C_Stanford_University.jpg/75px-Felix_Bloch%2C_Stanford_University.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Felix_Bloch%2C_Stanford_University.jpg/113px-Felix_Bloch%2C_Stanford_University.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Felix_Bloch%2C_Stanford_University.jpg/150px-Felix_Bloch%2C_Stanford_University.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Φέλιξ Μπλοχ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανάπτυξη νέων μεθόδων στα πυρηνικά μαγνητικά πειράματα ακριβείας, και για τις ανακαλύψεις που έγιναν σχετικά με αυτά»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Edward_Mills_Purcell.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Edward Mills Purcell.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Edward_Mills_Purcell.jpg/75px-Edward_Mills_Purcell.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Edward_Mills_Purcell.jpg/113px-Edward_Mills_Purcell.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Edward_Mills_Purcell.jpg/150px-Edward_Mills_Purcell.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Έντουαρντ Μιλς Πάρσελλ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1953</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Zernike.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Zernike.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Zernike.jpg/75px-Zernike.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Zernike.jpg/113px-Zernike.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Zernike.jpg/150px-Zernike.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Φριτς Φρέντερικ Ζερνίκε</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9F%CE%BB%CE%BB%CE%B1%CE%BD%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ολλανδία"><img alt="Flag of the Netherlands.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/23px-Flag_of_the_Netherlands.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/35px-Flag_of_the_Netherlands.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/45px-Flag_of_the_Netherlands.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ολλανδία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><br /></span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1954</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Max_Born.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Max Born.jpg" data-file-height="522" data-file-width="405" height="97" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Max_Born.jpg/75px-Max_Born.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Max_Born.jpg/113px-Max_Born.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Max_Born.jpg/150px-Max_Born.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μαξ Μπορν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη θεμελιώδη έρευνα στην Κβαντική μηχανική, ειδικότερα για τη στατιστική ερμηνεία της κυματοσυνάρτησης»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Bothe.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Bothe.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Bothe.jpg/75px-Bothe.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Bothe.jpg/113px-Bothe.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Bothe.jpg/150px-Bothe.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Βάλτερ Μπότε</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%94%CF%85%CF%84%CE%B9%CE%BA%CE%AE_%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Δυτική Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Δυτική Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμπτωτική μέθοδο και τις ανακαλύψεις που έγιναν σχετικά με αυτή»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1955</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Willis_Lamb_1955.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Willis Lamb 1955.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/77/Willis_Lamb_1955.jpg/75px-Willis_Lamb_1955.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Willis_Lamb_1955.jpg/113px-Willis_Lamb_1955.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Willis_Lamb_1955.jpg/150px-Willis_Lamb_1955.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γουίλις Γιουτζίν Λαμπ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις ανακαλύψεις του σχετικά με τη λεπτή υφή του φάσματος του υδρογόνου»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Polykarp_Kusch.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Polykarp Kusch.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Polykarp_Kusch.jpg/75px-Polykarp_Kusch.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Polykarp_Kusch.jpg/113px-Polykarp_Kusch.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Polykarp_Kusch.jpg/150px-Polykarp_Kusch.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πόλυκαρπ Κους</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: xx-small;">«για τον ακριβή προσδιορισμό της μαγνητικής ροπής του ηλεκτρονίου</span>»</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1956</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Bardeen.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Bardeen.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Bardeen.jpg/75px-Bardeen.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Bardeen.jpg/113px-Bardeen.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Bardeen.jpg/150px-Bardeen.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζον Μπαρντίν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις έρευνές τους επί των ημιαγωγών και για την ανακάλυψη του τρανζίστορ»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Brattain.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Brattain.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Brattain.jpg/75px-Brattain.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Brattain.jpg/113px-Brattain.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Brattain.jpg/150px-Brattain.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γουόλτερ Χάουζερ Μπράταιην</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:William_Shockley,_Stanford_University.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="William Shockley, Stanford University.jpg" data-file-height="250" data-file-width="200" height="94" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/William_Shockley%2C_Stanford_University.jpg/75px-William_Shockley%2C_Stanford_University.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/William_Shockley%2C_Stanford_University.jpg/113px-William_Shockley%2C_Stanford_University.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/William_Shockley%2C_Stanford_University.jpg/150px-William_Shockley%2C_Stanford_University.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γουίλλιαμ Μπράντφορντ Σόκλεϋ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1957</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τσουνγκ Ντάο Λι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A4%CE%B1%CF%8A%CE%B2%CE%AC%CE%BD" style="background: none; color: #0b0080;" title="Ταϊβάν"><img alt="Flag of the Republic of China.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/72/Flag_of_the_Republic_of_China.svg/23px-Flag_of_the_Republic_of_China.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Flag_of_the_Republic_of_China.svg/35px-Flag_of_the_Republic_of_China.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Flag_of_the_Republic_of_China.svg/45px-Flag_of_the_Republic_of_China.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a><span style="white-space: nowrap;">Δημοκρατία της Κίνας</span></span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη βαθιά έρευνα των λεγόμενων «νόμων ομοτιμίας» (parity laws), η οποία οδήγησε σε πολύ σημαντικές ανακαλύψεις σχετικά με τα στοιχειώδη σωματίδια»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:CNYang.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="CNYang.jpg" data-file-height="382" data-file-width="400" height="72" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/CNYang.jpg/75px-CNYang.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/CNYang.jpg/113px-CNYang.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/CNYang.jpg/150px-CNYang.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τσεν Νινγκ Γιανγκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A4%CE%B1%CF%8A%CE%B2%CE%AC%CE%BD" style="background: none; color: #0b0080;" title="Ταϊβάν"><img alt="Flag of the Republic of China.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/72/Flag_of_the_Republic_of_China.svg/23px-Flag_of_the_Republic_of_China.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Flag_of_the_Republic_of_China.svg/35px-Flag_of_the_Republic_of_China.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Flag_of_the_Republic_of_China.svg/45px-Flag_of_the_Republic_of_China.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Δημοκρατία της Κίνας</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1958</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Cerenkov.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Cerenkov.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Cerenkov.jpg/75px-Cerenkov.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Cerenkov.jpg/113px-Cerenkov.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Cerenkov.jpg/150px-Cerenkov.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πάβελ Αλεξέγιεβιτς Τσερενκόφ</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A3%CE%BF%CE%B2%CE%B9%CE%B5%CF%84%CE%B9%CE%BA%CE%AE_%CE%88%CE%BD%CF%89%CF%83%CE%B7" style="background: none; color: #0b0080;" title="Σοβιετική Ένωση"><img alt="Flag of the Soviet Union.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/23px-Flag_of_the_Soviet_Union.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/35px-Flag_of_the_Soviet_Union.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/46px-Flag_of_the_Soviet_Union.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Σοβιετική Ένωση</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη και την ερμηνεία του φαινομένου Τσερενκόφ-Βαβίλοφ»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Ilya_Frank.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Ilya Frank.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Ilya_Frank.jpg/75px-Ilya_Frank.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Ilya_Frank.jpg/113px-Ilya_Frank.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Ilya_Frank.jpg/150px-Ilya_Frank.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ίλια Φρανκ</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Igor_Tamm.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Igor Tamm.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Igor_Tamm.jpg/75px-Igor_Tamm.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Igor_Tamm.jpg/113px-Igor_Tamm.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Igor_Tamm.jpg/150px-Igor_Tamm.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ίγκορ Γιεβγκένιεβιτς Ταμ</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1959</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Owen_Chamberlain.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Owen Chamberlain.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/69/Owen_Chamberlain.jpg/75px-Owen_Chamberlain.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Owen_Chamberlain.jpg/113px-Owen_Chamberlain.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Owen_Chamberlain.jpg/150px-Owen_Chamberlain.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Όουεν Τσάμπερλεϊν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη του αντιπρωτονίου»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Segre.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Segre.jpg" data-file-height="2687" data-file-width="1919" height="105" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Segre.jpg/75px-Segre.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Segre.jpg/113px-Segre.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Segre.jpg/150px-Segre.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Εμίλιο Τζίνο Σεγκρέ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CF%84%CE%B1%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιταλία"><img alt="Flag of Italy.svg" class="thumbborder" data-file-height="1000" data-file-width="1500" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/23px-Flag_of_Italy.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/35px-Flag_of_Italy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/45px-Flag_of_Italy.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιταλία</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1960</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Donald_Glaser.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Donald Glaser.jpg" data-file-height="659" data-file-width="559" height="88" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/10/Donald_Glaser.jpg/75px-Donald_Glaser.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Donald_Glaser.jpg/113px-Donald_Glaser.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/Donald_Glaser.jpg/150px-Donald_Glaser.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ντόναλτ Άρθουρ Γκλέιζερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εφεύρεση του θαλάμου φυσαλίδων»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1961</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Robert_Hofstadter.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Robert Hofstadter.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Robert_Hofstadter.jpg/75px-Robert_Hofstadter.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Robert_Hofstadter.jpg/113px-Robert_Hofstadter.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Robert_Hofstadter.jpg/150px-Robert_Hofstadter.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ρόμπερτ Χόφσταντερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις πρωτότυπες μελέτες της σκέδασης ηλεκτρονίου από ατομικό πυρήνα, και για τις σχετικές ανακαλύψεις σχετικά με τη δομή των νουκλεονίων»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Mossbauer.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Mossbauer.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Mossbauer.jpg/75px-Mossbauer.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Mossbauer.jpg/113px-Mossbauer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Mossbauer.jpg/150px-Mossbauer.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ρούντολφ Λούντβιχ Μέσμπαουερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%94%CF%85%CF%84%CE%B9%CE%BA%CE%AE_%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Δυτική Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Δυτική Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: xx-small;">«για τις έρευνες σχετικά με την ακτινοβολία γάμμα και την ανακάλυψη του φαινομένου που πήρε το όνομά του». Δείτε: Φαινόμενο Μοσμπάουερ</span>»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1962</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Landau.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Landau.jpg" data-file-height="1527" data-file-width="1080" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Landau.jpg/75px-Landau.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Landau.jpg/113px-Landau.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Landau.jpg/150px-Landau.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Λεβ Νταβίντοβιτς Λαντάου</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A3%CE%BF%CE%B2%CE%B9%CE%B5%CF%84%CE%B9%CE%BA%CE%AE_%CE%88%CE%BD%CF%89%CF%83%CE%B7" style="background: none; color: #0b0080;" title="Σοβιετική Ένωση"><img alt="Flag of the Soviet Union.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/23px-Flag_of_the_Soviet_Union.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/35px-Flag_of_the_Soviet_Union.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/46px-Flag_of_the_Soviet_Union.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Σοβιετική Ένωση</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις πρωτότυπες θεωρίες του σχετικά με τη συμπυκνωμένη ύλη, και ειδικότερα για το υγρό ήλιο»</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1963</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Wigner.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Wigner.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Wigner.jpg/75px-Wigner.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Wigner.jpg/113px-Wigner.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Wigner.jpg/150px-Wigner.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γιουτζίν Γουίγκνερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9F%CF%85%CE%B3%CE%B3%CE%B1%CF%81%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ουγγαρία"><img alt="Flag of Hungary.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Flag_of_Hungary.svg/23px-Flag_of_Hungary.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Flag_of_Hungary.svg/35px-Flag_of_Hungary.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Flag_of_Hungary.svg/46px-Flag_of_Hungary.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ουγγαρία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή του στη θεωρία του ατομικού πυρήνα και των στοιχειωδών σωματιδίων, ειδικότερα μέσω της ανακάλυψης και εφαρμογής θεμελιωδών αρχών συμμετρίας»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Maria_Goeppert-Mayer.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Maria Goeppert-Mayer.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/22/Maria_Goeppert-Mayer.jpg/75px-Maria_Goeppert-Mayer.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Maria_Goeppert-Mayer.jpg/113px-Maria_Goeppert-Mayer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Maria_Goeppert-Mayer.jpg/150px-Maria_Goeppert-Mayer.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μαρία Γκέπερτ-Μάγιερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις ανακαλύψεις τους σχετικά με τη δομή των πυρηνικών φλοιών»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Johannes_Hans_Daniel_Jensen_(1907%E2%80%931973).jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Johannes Hans Daniel Jensen (1907–1973).jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Johannes_Hans_Daniel_Jensen_%281907%E2%80%931973%29.jpg/75px-Johannes_Hans_Daniel_Jensen_%281907%E2%80%931973%29.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Johannes_Hans_Daniel_Jensen_%281907%E2%80%931973%29.jpg/113px-Johannes_Hans_Daniel_Jensen_%281907%E2%80%931973%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Johannes_Hans_Daniel_Jensen_%281907%E2%80%931973%29.jpg/150px-Johannes_Hans_Daniel_Jensen_%281907%E2%80%931973%29.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τ. Χανς Ντ. Γιένσεν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1964</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Basov.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Basov.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Basov.jpg/75px-Basov.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Basov.jpg/113px-Basov.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Basov.jpg/150px-Basov.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Νικολάι Γκεννάντιεβιτς Μπάσοφ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A3%CE%BF%CE%B2%CE%B9%CE%B5%CF%84%CE%B9%CE%BA%CE%AE_%CE%88%CE%BD%CF%89%CF%83%CE%B7" style="background: none; color: #0b0080;" title="Σοβιετική Ένωση"><img alt="Flag of the Soviet Union.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/23px-Flag_of_the_Soviet_Union.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/35px-Flag_of_the_Soviet_Union.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/46px-Flag_of_the_Soviet_Union.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Σοβιετική Ένωση</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη θεμελιώδη εργασία τους στον τομέα της κβαντικής ηλεκτρονικής, η οποία οδήγησε στην κατασκευή ταλαντωτών και ενισχυτών βασισμένων στην αρχή Μέιζερ-λέιζερ»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Aleksandr_Prokhorov.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Aleksandr Prokhorov.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Aleksandr_Prokhorov.jpg/75px-Aleksandr_Prokhorov.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Aleksandr_Prokhorov.jpg/113px-Aleksandr_Prokhorov.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Aleksandr_Prokhorov.jpg/150px-Aleksandr_Prokhorov.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Αλεξάντρ Πρόχοροφ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A3%CE%BF%CE%B2%CE%B9%CE%B5%CF%84%CE%B9%CE%BA%CE%AE_%CE%88%CE%BD%CF%89%CF%83%CE%B7" style="background: none; color: #0b0080;" title="Σοβιετική Ένωση"><img alt="Flag of the Soviet Union.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/23px-Flag_of_the_Soviet_Union.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/35px-Flag_of_the_Soviet_Union.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/46px-Flag_of_the_Soviet_Union.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Σοβιετική Ένωση</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Charles_Hard_Townes-Nibib-2007-retouched.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Charles Hard Townes-Nibib-2007-retouched.jpg" data-file-height="792" data-file-width="448" height="133" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Charles_Hard_Townes-Nibib-2007-retouched.jpg/75px-Charles_Hard_Townes-Nibib-2007-retouched.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Charles_Hard_Townes-Nibib-2007-retouched.jpg/113px-Charles_Hard_Townes-Nibib-2007-retouched.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Charles_Hard_Townes-Nibib-2007-retouched.jpg/150px-Charles_Hard_Townes-Nibib-2007-retouched.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τσαρλς Χαρντ Τάουνς</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1965</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:RichardFeynman-PaineMansionWoods1984_copyrightTamikoThiel_bw.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="RichardFeynman-PaineMansionWoods1984 copyrightTamikoThiel bw.jpg" data-file-height="541" data-file-width="470" height="86" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/RichardFeynman-PaineMansionWoods1984_copyrightTamikoThiel_bw.jpg/75px-RichardFeynman-PaineMansionWoods1984_copyrightTamikoThiel_bw.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/RichardFeynman-PaineMansionWoods1984_copyrightTamikoThiel_bw.jpg/113px-RichardFeynman-PaineMansionWoods1984_copyrightTamikoThiel_bw.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/RichardFeynman-PaineMansionWoods1984_copyrightTamikoThiel_bw.jpg/150px-RichardFeynman-PaineMansionWoods1984_copyrightTamikoThiel_bw.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ρίτσαρντ Φίλλιπς Φάινμαν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη θεμελιώδη τους εργασία στον τομέα της κβαντικής ηλεκτροδυναμικής, με βαθιές συνέπειες στη Σωματιδιακή Φυσική»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Schwinger.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Schwinger.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Schwinger.jpg/75px-Schwinger.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Schwinger.jpg/113px-Schwinger.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Schwinger.jpg/150px-Schwinger.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζούλιαν Σβίνγκερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Tomonaga.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Tomonaga.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Tomonaga.jpg/75px-Tomonaga.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Tomonaga.jpg/113px-Tomonaga.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Tomonaga.jpg/150px-Tomonaga.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σιν-Ιτίρο Τομονάγκα,</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B1%CF%80%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιαπωνία"><img alt="Flag of Japan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/23px-Flag_of_Japan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/35px-Flag_of_Japan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/45px-Flag_of_Japan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιαπωνία</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1966</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Kastler.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Kastler.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Kastler.jpg/75px-Kastler.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Kastler.jpg/113px-Kastler.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Kastler.jpg/150px-Kastler.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Αλφρέντ Καστλέρ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη και εξέλιξη οπτικών μεθόδων για τη μελέτη των ερτζιανών συντονισμών των ατόμων»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1967</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Hans_Bethe.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Hans Bethe.jpg" data-file-height="549" data-file-width="382" height="108" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Hans_Bethe.jpg/75px-Hans_Bethe.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Hans_Bethe.jpg/113px-Hans_Bethe.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Hans_Bethe.jpg/150px-Hans_Bethe.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χανς Αλμπρεχτ Μπέτε</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή του επί των πυρηνικών διεργασιών, ειδικότερα για τις ανακαλύψεις σχετικά με την παραγωγή ενέργειας στα άστρα»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1968</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Luis_Alvarez_ID_badge.png" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Luis Alvarez ID badge.png" data-file-height="175" data-file-width="130" height="101" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Luis_Alvarez_ID_badge.png/75px-Luis_Alvarez_ID_badge.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Luis_Alvarez_ID_badge.png/113px-Luis_Alvarez_ID_badge.png 1.5x, //upload.wikimedia.org/wikipedia/commons/b/b9/Luis_Alvarez_ID_badge.png 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Λούις Άλβαρεζ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή του στη Σωματιδιακή Φυσική, ειδικότερα για την ανακάλυψη ενός μεγάλου αριθμού καταστάσεων συντονισμού»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1969</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Murray_Gell-Mann.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Murray Gell-Mann.jpg" data-file-height="1103" data-file-width="949" height="87" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/87/Murray_Gell-Mann.jpg/75px-Murray_Gell-Mann.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Murray_Gell-Mann.jpg/113px-Murray_Gell-Mann.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Murray_Gell-Mann.jpg/150px-Murray_Gell-Mann.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μάρεϋ Γκελ-Μαν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή του και τις ανακαλύψεις σχετικά με την κατηγοριοποίηση των στοιχειωδών σωματιδίων και τις αλληλεπιδράσεις τους»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1970</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:YoungAlfven.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="YoungAlfven.jpg" data-file-height="1744" data-file-width="1256" height="104" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/YoungAlfven.jpg/75px-YoungAlfven.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/YoungAlfven.jpg/113px-YoungAlfven.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/YoungAlfven.jpg/150px-YoungAlfven.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χανς Όλοφ Γκόστα Αλφβέν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A3%CE%BF%CF%85%CE%B7%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Σουηδία"><img alt="Flag of Sweden.svg" class="thumbborder" data-file-height="1000" data-file-width="1600" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/23px-Flag_of_Sweden.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/35px-Flag_of_Sweden.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/46px-Flag_of_Sweden.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Σουηδία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη θεμελιώδη εργασία του και τις ανακαλύψεις του στη Μαγνητοϋδροδυναμική, με ποικίλες εφαρμογές σε διαφορετικά πεδία της Φυσικής Πλάσματος»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Louis_Neel_1970.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Louis Neel 1970.jpg" data-file-height="3000" data-file-width="1965" height="115" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Louis_Neel_1970.jpg/75px-Louis_Neel_1970.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Louis_Neel_1970.jpg/113px-Louis_Neel_1970.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Louis_Neel_1970.jpg/150px-Louis_Neel_1970.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Λουί Νεέλ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη θεμελιώδη εργασία του και τις ανακαλύψεις σχετικά με τον σιδηρομαγνητισμό και τον παραμαγνητισμό, οι οποίες οδήγησαν σε σημαντικές εφαρμογές στη Φυσική στερεάς κατάστασης»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1971</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ντένις Γκέιμπορ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εφεύρεση και εξέλιξη της ολογραφικής μεθόδου»</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1972</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Bardeen.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Bardeen.jpg" data-file-height="396" data-file-width="280" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Bardeen.jpg/75px-Bardeen.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Bardeen.jpg/113px-Bardeen.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Bardeen.jpg/150px-Bardeen.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζον Μπαρντίν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την από κοινού εξέλιξη της θεωρίας της υπεραγωγιμότητας, (Θεωρία BCS)».</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Nobel_Laureate_Leon_Cooper_in_2007.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Nobel Laureate Leon Cooper in 2007.jpg" data-file-height="1659" data-file-width="2000" height="62" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Nobel_Laureate_Leon_Cooper_in_2007.jpg/75px-Nobel_Laureate_Leon_Cooper_in_2007.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Nobel_Laureate_Leon_Cooper_in_2007.jpg/113px-Nobel_Laureate_Leon_Cooper_in_2007.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Nobel_Laureate_Leon_Cooper_in_2007.jpg/150px-Nobel_Laureate_Leon_Cooper_in_2007.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Λέον Νιλ Κούπερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:John_Robert_Schrieffer.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="John Robert Schrieffer.jpg" data-file-height="141" data-file-width="100" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/86/John_Robert_Schrieffer.jpg/75px-John_Robert_Schrieffer.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/8/86/John_Robert_Schrieffer.jpg 1.5x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζον Ρόμπερτ Σρίφερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1973</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Λέο Εσάκι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B1%CF%80%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιαπωνία"><img alt="Flag of Japan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/23px-Flag_of_Japan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/35px-Flag_of_Japan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/45px-Flag_of_Japan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιαπωνία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις πειραματικές ανακαλύψεις τους σχετικά με το Φαινόμενο Σήραγγας σε ημιαγωγούς και υπεραγωγούς»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Ivar_Giaever.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Ivar Giaever.jpg" data-file-height="799" data-file-width="610" height="98" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Ivar_Giaever.jpg/75px-Ivar_Giaever.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Ivar_Giaever.jpg/113px-Ivar_Giaever.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Ivar_Giaever.jpg/150px-Ivar_Giaever.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ίβαρ Γκιέβερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α<br />Νορβηγία</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μπράιαν Τζόζεφσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9F%CF%85%CE%B1%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ουαλία"><img alt="Flag of Wales.svg" class="thumbborder" data-file-height="800" data-file-width="1200" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Flag_of_Wales.svg/23px-Flag_of_Wales.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Flag_of_Wales.svg/35px-Flag_of_Wales.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Flag_of_Wales.svg/45px-Flag_of_Wales.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ουαλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις θεωρητικές προβλέψεις των ιδιοτήτων ενός υπεραγωγού, ειδικότερα για τα φαινόμενα που είναι γνωστά ως φαινόμενα Τζόζεφσον»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1974</span></td><td rowspan="2"></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μάρτιν Ράιλ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την πρωτότυπη εργασία τους στη Ραδιοαστροφυσική: Ο Ράιλ για τις παρατηρήσεις και τις εφευρέσεις του, ο Χιούις για τον σημαντικό ρόλο στην ανακάλυψη των πάλσαρ»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Άντονι Χίουις</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1975</span></td><td rowspan="3"></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Άαγκε Μπορ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Δανία"><img alt="Flag of Denmark.svg" class="thumbborder" data-file-height="560" data-file-width="740" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Flag_of_Denmark.svg/20px-Flag_of_Denmark.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Flag_of_Denmark.svg/31px-Flag_of_Denmark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Flag_of_Denmark.svg/40px-Flag_of_Denmark.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="20" /></a> Δανία</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της συσχέτισης μεταξύ της ολικής και της σωματιδιακής κίνησης στον ατομικό πυρήνα, και για την εξέλιξη της θεωρίας της δομής των ατομικών πυρήνων βασισμένη στην παραπάνω συσχέτιση»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μπεν Ρόι Μότελσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Δανία"><img alt="Flag of Denmark.svg" class="thumbborder" data-file-height="560" data-file-width="740" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Flag_of_Denmark.svg/20px-Flag_of_Denmark.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Flag_of_Denmark.svg/31px-Flag_of_Denmark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Flag_of_Denmark.svg/40px-Flag_of_Denmark.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="20" /></a> Δανία</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Λέο Τζέιμς Ρέινγουότερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1976</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Burton_Richter_-_charm_quark.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Burton Richter - charm quark.jpg" data-file-height="150" data-file-width="125" height="90" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/79/Burton_Richter_-_charm_quark.jpg/75px-Burton_Richter_-_charm_quark.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Burton_Richter_-_charm_quark.jpg/113px-Burton_Richter_-_charm_quark.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/7/79/Burton_Richter_-_charm_quark.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μπάρτον Ρίχτερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την πρωτότυπη εργασία τους στην ανακάλυψη ενός βαρέος στοιχειώδους σωματίου νέου είδους. Συγκεκριμένα, για την ανακάλυψη του J/Ψ σωματιδίου και για την επιβεβαίωση της ιδέας ότι η βαρυονική ύλη (όπως το πρωτόνιο και το νετρόνιο) είναι φταγμένη από κουάρκ»</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σάμιουελ Τσάο Τσουνγκ Τινγκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1977</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Andersonphoto.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Andersonphoto.jpg" data-file-height="701" data-file-width="586" height="90" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Andersonphoto.jpg/75px-Andersonphoto.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Andersonphoto.jpg/113px-Andersonphoto.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Andersonphoto.jpg/150px-Andersonphoto.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Φίλιπ Γουόρεν Άντερσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις θεμελιώδεις θεωρητικές έρευνες της ηλεκτρονιακής δομής μαγνητικών και διαταραγμένων συστημάτων»</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Νέβιλ Φράνσις Μοτ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζον Χάσμπρουκ βαν Βλεκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1978</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:KustodiyevSemenov_Kapitsa.JPG" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="KustodiyevSemenov Kapitsa.JPG" data-file-height="1200" data-file-width="1188" height="76" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/KustodiyevSemenov_Kapitsa.JPG/75px-KustodiyevSemenov_Kapitsa.JPG" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/KustodiyevSemenov_Kapitsa.JPG/113px-KustodiyevSemenov_Kapitsa.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b2/KustodiyevSemenov_Kapitsa.JPG/150px-KustodiyevSemenov_Kapitsa.JPG 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πιοτρ Λεονίντοβιτς Καπίτσα</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A3%CE%BF%CE%B2%CE%B9%CE%B5%CF%84%CE%B9%CE%BA%CE%AE_%CE%88%CE%BD%CF%89%CF%83%CE%B7" style="background: none; color: #0b0080;" title="Σοβιετική Ένωση"><img alt="Flag of the Soviet Union.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/23px-Flag_of_the_Soviet_Union.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/35px-Flag_of_the_Soviet_Union.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Flag_of_the_Soviet_Union.svg/46px-Flag_of_the_Soviet_Union.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Σοβιετική Ένωση</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις βασικές εφευρέσεις και ανακαλύψεις στον τομέα της Φυσικής χαμηλών θερμοκρασιών»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Arno_Penzias.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Arno Penzias.jpg" data-file-height="375" data-file-width="449" height="63" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/75/Arno_Penzias.jpg/75px-Arno_Penzias.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Arno_Penzias.jpg/113px-Arno_Penzias.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Arno_Penzias.jpg/150px-Arno_Penzias.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Άρνο Άλαν Πενζίας</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της ακτινοβολίας υποβάθρου στην περιοχή των μικροκυμάτων»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Wilson_penzias200.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Wilson penzias200.jpg" data-file-height="309" data-file-width="350" height="66" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Wilson_penzias200.jpg/75px-Wilson_penzias200.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Wilson_penzias200.jpg/113px-Wilson_penzias200.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Wilson_penzias200.jpg/150px-Wilson_penzias200.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ρόμπερτ Γούντροου Γουίλσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1979</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Sheldon_Glashow_at_Harvard.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Sheldon Glashow at Harvard.jpg" data-file-height="472" data-file-width="240" height="148" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/36/Sheldon_Glashow_at_Harvard.jpg/75px-Sheldon_Glashow_at_Harvard.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Sheldon_Glashow_at_Harvard.jpg/113px-Sheldon_Glashow_at_Harvard.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/Sheldon_Glashow_at_Harvard.jpg/150px-Sheldon_Glashow_at_Harvard.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σέλντον Λι Γκλάσοου</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή τους στη θεωρία των ενοποιημένων ηλεκτρασθενών αλληλεπιδράσεων των στοιχειωδών σωματιδίων, η οποία συμπεριλάμβανε μεταξύ άλλων και την πρόβλεψη των φορέων της ασθενούς αλληλεπίδρασης, τα W και Ζ μποζόνια»</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Αμπντούς Σαλάμ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A0%CE%B1%CE%BA%CE%B9%CF%83%CF%84%CE%AC%CE%BD" style="background: none; color: #0b0080;" title="Πακιστάν"><img alt="Flag of Pakistan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/32/Flag_of_Pakistan.svg/23px-Flag_of_Pakistan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Flag_of_Pakistan.svg/35px-Flag_of_Pakistan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Flag_of_Pakistan.svg/45px-Flag_of_Pakistan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Πακιστάν</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Steven-weinberg.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Steven-weinberg.jpg" data-file-height="477" data-file-width="386" height="93" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/91/Steven-weinberg.jpg/75px-Steven-weinberg.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Steven-weinberg.jpg/113px-Steven-weinberg.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Steven-weinberg.jpg/150px-Steven-weinberg.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Στίβεν Βάινμπεργκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1980</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:James_Watson_Cronin_2006.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="James Watson Cronin 2006.jpg" data-file-height="1536" data-file-width="2048" height="56" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a6/James_Watson_Cronin_2006.jpg/75px-James_Watson_Cronin_2006.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/James_Watson_Cronin_2006.jpg/113px-James_Watson_Cronin_2006.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/James_Watson_Cronin_2006.jpg/150px-James_Watson_Cronin_2006.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζέιμς Γουότσον Κρόνιν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη των παραβιάσεων θεμελιωδών αρχών συμμετρίας στην καταστροφή των ουδέτερωνΚ-μεσονίων»</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Βαλ Λόγκτσον Φιτς</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1981</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Nico_2006_Tucson_Wiki.png" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Nico 2006 Tucson Wiki.png" data-file-height="491" data-file-width="400" height="92" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/90/Nico_2006_Tucson_Wiki.png/75px-Nico_2006_Tucson_Wiki.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Nico_2006_Tucson_Wiki.png/113px-Nico_2006_Tucson_Wiki.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Nico_2006_Tucson_Wiki.png/150px-Nico_2006_Tucson_Wiki.png 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Νίκολας Μπλέμπεργκεν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή τους στην εξέλιξη της Φασματοσκοπίας με λέιζερ»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Artur_Schawlow,_Stanford_University.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Artur Schawlow, Stanford University.jpg" data-file-height="250" data-file-width="200" height="94" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Artur_Schawlow%2C_Stanford_University.jpg/75px-Artur_Schawlow%2C_Stanford_University.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Artur_Schawlow%2C_Stanford_University.jpg/113px-Artur_Schawlow%2C_Stanford_University.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/Artur_Schawlow%2C_Stanford_University.jpg/150px-Artur_Schawlow%2C_Stanford_University.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><a class="new" href="https://el.wikipedia.org/w/index.php?title=%CE%86%CF%81%CE%B8%CE%BF%CF%85%CF%81_%CE%9B%CE%AD%CE%BF%CE%BD%CE%B1%CF%81%CE%BD%CF%84_%CE%A3%CF%8C%CE%BF%CF%85%CE%BB%CE%BF%CE%BF%CF%85&action=edit&redlink=1" style="background: none; color: #a55858;" title="Άρθουρ Λέοναρντ Σόουλοου (δεν έχει γραφτεί ακόμα)"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Άρθουρ Λέοναρντ Σόουλοου</span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> <a class="mw-redirect" href="https://el.wikipedia.org/wiki/%CE%97.%CE%A0.%CE%91" style="background: none; color: #0b0080;" title="Η.Π.Α">Η.Π.Α</a></span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Κάι Μαν Μπέργε Σίγκμπαν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A3%CE%BF%CF%85%CE%B7%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Σουηδία"><img alt="Flag of Sweden.svg" class="thumbborder" data-file-height="1000" data-file-width="1600" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/23px-Flag_of_Sweden.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/35px-Flag_of_Sweden.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Flag_of_Sweden.svg/46px-Flag_of_Sweden.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Σουηδία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή του στην εξέλιξη της υψηλής ανάλυσης ηλεκτρονικής φασματοσκοπίας»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1982</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Κένεθ Τ. Γουίλσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη θεωρία των κρίσιμων φαινομένων, σε συσχέτιση με τις μετατροπές φάσεων»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1983</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σουμπραμανιάν Τσαντρασεχάρ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%BD%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ινδία"><img alt="Flag of India.svg" class="thumbborder" data-file-height="900" data-file-width="1350" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_India.svg/23px-Flag_of_India.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_India.svg/35px-Flag_of_India.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Flag_of_India.svg/45px-Flag_of_India.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ινδία/<a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις θεωρητικές μελέτες των φυσικών διεργασιών της δομής και της εξέλιξης των άστρων. Δες Όριο Τσαντρασεκάρ»</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γουίλιαμ Άλφρεντ Φάουλερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις θεωρητικές και πειραματικές μελέτες των πυρηνικών διεργασιών στον σχηματισμό των χημικών στοιχείων στο Σύμπαν»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1984</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Carlo_Rubbia_W_and_Z_bosons.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Carlo Rubbia W and Z bosons.jpg" data-file-height="150" data-file-width="125" height="90" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Carlo_Rubbia_W_and_Z_bosons.jpg/75px-Carlo_Rubbia_W_and_Z_bosons.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Carlo_Rubbia_W_and_Z_bosons.jpg/113px-Carlo_Rubbia_W_and_Z_bosons.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/7/7a/Carlo_Rubbia_W_and_Z_bosons.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Κάρλο Ρούμπια</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CF%84%CE%B1%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιταλία"><img alt="Flag of Italy.svg" class="thumbborder" data-file-height="1000" data-file-width="1500" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/23px-Flag_of_Italy.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/35px-Flag_of_Italy.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Flag_of_Italy.svg/45px-Flag_of_Italy.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιταλία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις σημαντικές συμβολές τους, που οδήγησαν στην ανακάλυψη των σωματιδιακών πεδίων W και Ζ, φορέων της ασθενούς αλληλεπίδρασης»</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σιμόν βαν ντερ Μέερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9F%CE%BB%CE%BB%CE%B1%CE%BD%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ολλανδία"><img alt="Flag of the Netherlands.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/23px-Flag_of_the_Netherlands.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/35px-Flag_of_the_Netherlands.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/45px-Flag_of_the_Netherlands.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ολλανδία</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1985</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Klausvonklitzing.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Klausvonklitzing.jpg" data-file-height="1742" data-file-width="1200" height="109" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Klausvonklitzing.jpg/75px-Klausvonklitzing.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Klausvonklitzing.jpg/113px-Klausvonklitzing.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Klausvonklitzing.jpg/150px-Klausvonklitzing.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Κλάους φον Κλίτσινγκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%94%CF%85%CF%84%CE%B9%CE%BA%CE%AE_%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Δυτική Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Δυτική Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη του Κβαντικού Φαινόμενου Hall»</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1986</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ερνστ Ρούσκα</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%94%CF%85%CF%84%CE%B9%CE%BA%CE%AE_%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Δυτική Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Δυτική Γερμανία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη θεμελιώδη εργασία του στην ηλεκτρονική Οπτική, και για τον σχεδιασμό του πρώτου ηλεκτρονικού μικροσκοπίου»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Gerd_Binnig_sw.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Gerd Binnig sw.jpg" data-file-height="708" data-file-width="531" height="100" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Gerd_Binnig_sw.jpg/75px-Gerd_Binnig_sw.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Gerd_Binnig_sw.jpg/113px-Gerd_Binnig_sw.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Gerd_Binnig_sw.jpg/150px-Gerd_Binnig_sw.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γκέρντ Μπίνιχ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%94%CF%85%CF%84%CE%B9%CE%BA%CE%AE_%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Δυτική Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Δυτική Γερμανία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τον σχεδιασμό του μικροσκοπίου ανιχνευτή σήραγγας <i>(scanning tunneling microscope)</i>»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Rohrer.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Rohrer.jpg" data-file-height="200" data-file-width="200" height="75" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/32/Rohrer.jpg/75px-Rohrer.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Rohrer.jpg/113px-Rohrer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Rohrer.jpg/150px-Rohrer.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χάινριχ Ρόρερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BB%CE%B2%CE%B5%CF%84%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ελβετία"><img alt="Flag of Switzerland.svg" class="thumbborder" data-file-height="1000" data-file-width="1000" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/15px-Flag_of_Switzerland.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/23px-Flag_of_Switzerland.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/30px-Flag_of_Switzerland.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="15" /></a> Ελβετία</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1987</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Ibmgb.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Ibmgb.jpg" data-file-height="500" data-file-width="332" height="113" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/81/Ibmgb.jpg/75px-Ibmgb.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Ibmgb.jpg/113px-Ibmgb.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Ibmgb.jpg/150px-Ibmgb.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γιοχάνες Γκέοργκ Μπέντορτς</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%94%CF%85%CF%84%CE%B9%CE%BA%CE%AE_%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Δυτική Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Δυτική Γερμανία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη σημαντική ανακάλυψη της υπεραγωγιμότητας σε κεραμικά υλικά»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Karl_Alexander_Mueller.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Karl Alexander Mueller.jpg" data-file-height="334" data-file-width="403" height="62" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Karl_Alexander_Mueller.jpg/75px-Karl_Alexander_Mueller.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Karl_Alexander_Mueller.jpg/113px-Karl_Alexander_Mueller.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Karl_Alexander_Mueller.jpg/150px-Karl_Alexander_Mueller.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><a class="new" href="https://el.wikipedia.org/w/index.php?title=%CE%9A%CE%B1%CF%81%CE%BB_%CE%91%CE%BB%CE%B5%CE%BE%CE%AC%CE%BD%CF%84%CE%B5%CF%81_%CE%9C%CE%AF%CE%BB%CE%B5%CF%81&action=edit&redlink=1" style="background: none; color: #a55858;" title="Καρλ Αλεξάντερ Μίλερ (δεν έχει γραφτεί ακόμα)"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Καρλ Αλεξάντερ Μίλερ</span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BB%CE%B2%CE%B5%CF%84%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ελβετία"><img alt="Flag of Switzerland.svg" class="thumbborder" data-file-height="1000" data-file-width="1000" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/15px-Flag_of_Switzerland.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/23px-Flag_of_Switzerland.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Switzerland.svg/30px-Flag_of_Switzerland.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="15" /></a> Ελβετία</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1988</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Leon_M._Lederman.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Leon M. Lederman.jpg" data-file-height="768" data-file-width="1024" height="56" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Leon_M._Lederman.jpg/75px-Leon_M._Lederman.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Leon_M._Lederman.jpg/113px-Leon_M._Lederman.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Leon_M._Lederman.jpg/150px-Leon_M._Lederman.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Λέον Μαξ Λέντερμαν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη μέθοδο ακτινοβολίας νετρίνου και για την αποσαφήνιση της διπλέτας των λεπτονίων μέσω της ανακάλυψης του νετρίνου του μιονίου»</span></td></tr>
<tr><td></td><td><a class="new" href="https://el.wikipedia.org/w/index.php?title=%CE%9C%CE%AD%CE%BB%CE%B2%CE%B9%CE%BD_%CE%A3%CE%B2%CE%B1%CF%81%CF%84%CF%82&action=edit&redlink=1" style="background: none; color: #a55858;" title="Μέλβιν Σβαρτς (δεν έχει γραφτεί ακόμα)"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μέλβιν Σβαρτς</span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Jack-Steinberger-2008.JPG" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Jack-Steinberger-2008.JPG" data-file-height="1221" data-file-width="864" height="106" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/42/Jack-Steinberger-2008.JPG/75px-Jack-Steinberger-2008.JPG" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Jack-Steinberger-2008.JPG/113px-Jack-Steinberger-2008.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Jack-Steinberger-2008.JPG/150px-Jack-Steinberger-2008.JPG 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><a class="new" href="https://el.wikipedia.org/w/index.php?title=%CE%A4%CE%B6%CE%B1%CE%BA_%CE%A3%CF%84%CE%AC%CE%B9%CE%BD%CE%BC%CF%80%CE%B5%CF%81%CE%B3%CE%BA%CE%B5%CF%81&action=edit&redlink=1" style="background: none; color: #a55858;" title="Τζακ Στάινμπεργκερ (δεν έχει γραφτεί ακόμα)"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζακ Στάινμπεργκερ</span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1989</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Νόρμαν Φόστερ Ράμσεϋ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εφεύρεση της μεθόδου απομονωμένων ταλαντωτικών πεδίων και για τη χρήση της σε ατομικά ρολόγια»</span></td></tr>
<tr><td rowspan="2"></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χανς Γκοργκ Ντέμελτ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εξέλιξη της τεχνικής της παγίδας ιονισμού»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Βόλφγκανγκ Πάουλ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%94%CF%85%CF%84%CE%B9%CE%BA%CE%AE_%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Δυτική Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Δυτική Γερμανία</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1990</span></td><td rowspan="3"></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζερόμ Ισαάκ Φρίντμαν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις πρωτότυπες έρευνες σχετικά με τη βαθιά ανελαστική σκέδαση ηλεκτρονίων σε πρωτόνια και δέσμια νετρόνια, οι οποίες ήταν πολύ σημαντικές για την εξέλιξη του μοντέλου των κουάρκ στη Σωματιδιακή Φυσική»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χένρι Γουέι Κένταλ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ρίτσαρντ Έντουαρντ Τέιλορ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%B1%CE%BD%CE%B1%CE%B4%CE%AC%CF%82" style="background: none; color: #0b0080;" title="Καναδάς"><img alt="Flag of Canada.svg" class="thumbborder" data-file-height="500" data-file-width="1000" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/23px-Flag_of_Canada.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/35px-Flag_of_Canada.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/46px-Flag_of_Canada.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Καναδάς</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1991</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Pierre-Gilles_Rice_University.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Pierre-Gilles Rice University.jpg" data-file-height="900" data-file-width="599" height="113" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Pierre-Gilles_Rice_University.jpg/75px-Pierre-Gilles_Rice_University.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Pierre-Gilles_Rice_University.jpg/113px-Pierre-Gilles_Rice_University.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Pierre-Gilles_Rice_University.jpg/150px-Pierre-Gilles_Rice_University.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πιερ-Ζιλ ντε Ζεν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη ότι οι μέθοδοι που αναπτύχθηκαν για τη μελέτη φαινομένων σε απλά συστήματα μπορούν να γενικευθούν για πιο πολύπλοκες μορφές της ύλης, ειδικότερα σε υγρούς κρυστάλλους και πολυμερή»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1992</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:CHARPAK_Georges-24x50-2005_cropped.JPG" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="CHARPAK Georges-24x50-2005 cropped.JPG" data-file-height="250" data-file-width="222" height="84" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f6/CHARPAK_Georges-24x50-2005_cropped.JPG/75px-CHARPAK_Georges-24x50-2005_cropped.JPG" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/CHARPAK_Georges-24x50-2005_cropped.JPG/113px-CHARPAK_Georges-24x50-2005_cropped.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f6/CHARPAK_Georges-24x50-2005_cropped.JPG/150px-CHARPAK_Georges-24x50-2005_cropped.JPG 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ζωρζ Σαρπάκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εφεύρεση και την ανάπτυξη των ανιχνευτών σωματιδίων»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1993</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ράσελ Άλαν Χαλς</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη ενός νέου τύπου πάλσαρ, η οποία άνοιξε νέες προοπτικές για τη μελέτη της βαρύτητας»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:2008JosephTaylor.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="2008JosephTaylor.jpg" data-file-height="909" data-file-width="777" height="88" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/14/2008JosephTaylor.jpg/75px-2008JosephTaylor.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/2008JosephTaylor.jpg/113px-2008JosephTaylor.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/2008JosephTaylor.jpg/150px-2008JosephTaylor.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζόσεφ Χούτον Τέιλορ.</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1994</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Bertram_Brockhouse.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Bertram Brockhouse.jpg" data-file-height="499" data-file-width="413" height="91" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Bertram_Brockhouse.jpg/75px-Bertram_Brockhouse.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Bertram_Brockhouse.jpg/113px-Bertram_Brockhouse.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Bertram_Brockhouse.jpg/150px-Bertram_Brockhouse.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μπέρτραμ Νέβιλ Μπρόκχαους</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%B1%CE%BD%CE%B1%CE%B4%CE%AC%CF%82" style="background: none; color: #0b0080;" title="Καναδάς"><img alt="Flag of Canada.svg" class="thumbborder" data-file-height="500" data-file-width="1000" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/23px-Flag_of_Canada.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/35px-Flag_of_Canada.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/46px-Flag_of_Canada.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Καναδάς</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανάπτυξη της φασματοσκοπίας των νετρονίων»</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Κλίφορντ Γκλένγουντ Σαλ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανάπτυξη της τεχνικής απορρόφησης νετρονίων (neutron diffraction)»</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1995</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Martin_Perl_-_tau.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Martin Perl - tau.jpg" data-file-height="150" data-file-width="125" height="90" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/65/Martin_Perl_-_tau.jpg/75px-Martin_Perl_-_tau.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Martin_Perl_-_tau.jpg/113px-Martin_Perl_-_tau.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/6/65/Martin_Perl_-_tau.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μάρτιν Λιούις Περλ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη του λεπτονίου ταυ»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Frederick_Reines.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Frederick Reines.jpg" data-file-height="430" data-file-width="350" height="92" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/72/Frederick_Reines.jpg/75px-Frederick_Reines.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Frederick_Reines.jpg/113px-Frederick_Reines.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Frederick_Reines.jpg/150px-Frederick_Reines.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Φρέντερικ Ράινες</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανίχνευση του νετρίνου»</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1996</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ντέιβιντ Μόρις Λι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της υπερρευστότητας στο ήλιο-3»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Douglas_Osheroff.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Douglas Osheroff.jpg" data-file-height="599" data-file-width="452" height="99" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Douglas_Osheroff.jpg/75px-Douglas_Osheroff.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Douglas_Osheroff.jpg/113px-Douglas_Osheroff.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Douglas_Osheroff.jpg/150px-Douglas_Osheroff.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ντάγκλας Ντιν Όσεροφ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Robert_Coleman_Richardson.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Robert Coleman Richardson.jpg" data-file-height="273" data-file-width="253" height="81" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Robert_Coleman_Richardson.jpg/75px-Robert_Coleman_Richardson.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Robert_Coleman_Richardson.jpg/113px-Robert_Coleman_Richardson.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Robert_Coleman_Richardson.jpg/150px-Robert_Coleman_Richardson.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ρόμπερτ Κόλμαν Ρίτσαρντσον</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1997</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Steven_Chu_official_portrait_headshot.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Steven Chu official portrait headshot.jpg" data-file-height="850" data-file-width="669" height="95" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/28/Steven_Chu_official_portrait_headshot.jpg/75px-Steven_Chu_official_portrait_headshot.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Steven_Chu_official_portrait_headshot.jpg/113px-Steven_Chu_official_portrait_headshot.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Steven_Chu_official_portrait_headshot.jpg/150px-Steven_Chu_official_portrait_headshot.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Στίβεν Τσου</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανάπτυξη των μεθόδων ψύξης και παγίδευσης ατόμων με ακτίνες λέιζερ»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Claude_Cohen-Tannoudji.JPG" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Claude Cohen-Tannoudji.JPG" data-file-height="758" data-file-width="790" height="72" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Claude_Cohen-Tannoudji.JPG/75px-Claude_Cohen-Tannoudji.JPG" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Claude_Cohen-Tannoudji.JPG/113px-Claude_Cohen-Tannoudji.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Claude_Cohen-Tannoudji.JPG/150px-Claude_Cohen-Tannoudji.JPG 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Κλοντ Κοέν-Τανούτζι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:William_Phillips-physicist_photo.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="William Phillips-physicist photo.jpg" data-file-height="450" data-file-width="302" height="112" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c7/William_Phillips-physicist_photo.jpg/75px-William_Phillips-physicist_photo.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/William_Phillips-physicist_photo.jpg/113px-William_Phillips-physicist_photo.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c7/William_Phillips-physicist_photo.jpg/150px-William_Phillips-physicist_photo.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γουίλλιαμ Ντάνιελ Φίλιπς</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1998</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Robert_Laughlin,_Stanford_University.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Robert Laughlin, Stanford University.jpg" data-file-height="250" data-file-width="200" height="94" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Robert_Laughlin%2C_Stanford_University.jpg/75px-Robert_Laughlin%2C_Stanford_University.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Robert_Laughlin%2C_Stanford_University.jpg/113px-Robert_Laughlin%2C_Stanford_University.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Robert_Laughlin%2C_Stanford_University.jpg/150px-Robert_Laughlin%2C_Stanford_University.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ρόμπερτ Μ. Λόλιν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη μιας νέας μορφής κβαντικού ρευστού με ελαφρώς φορτισμένες διεγέρσεις»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Horst_St%C3%B6rmer.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Horst Störmer.jpg" data-file-height="2026" data-file-width="1121" height="136" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/24/Horst_St%C3%B6rmer.jpg/75px-Horst_St%C3%B6rmer.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Horst_St%C3%B6rmer.jpg/113px-Horst_St%C3%B6rmer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Horst_St%C3%B6rmer.jpg/150px-Horst_St%C3%B6rmer.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χορστ Λούντβιχ Στέρμερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ντανιέλ Τσι Τσούι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">1999</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:GerardtHooft.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="GerardtHooft.jpg" data-file-height="335" data-file-width="239" height="105" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cc/GerardtHooft.jpg/75px-GerardtHooft.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/GerardtHooft.jpg/113px-GerardtHooft.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/GerardtHooft.jpg/150px-GerardtHooft.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γκεράρντους Xουφτ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9F%CE%BB%CE%BB%CE%B1%CE%BD%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ολλανδία"><img alt="Flag of the Netherlands.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/23px-Flag_of_the_Netherlands.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/35px-Flag_of_the_Netherlands.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/45px-Flag_of_the_Netherlands.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ολλανδία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την αποσαφήνιση της κβαντικής δομής των ηλεκτρασθενών αλληλεπιδράσεων στη Φυσική»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Martinus_Veltman.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Martinus Veltman.jpg" data-file-height="445" data-file-width="334" height="100" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Martinus_Veltman.jpg/75px-Martinus_Veltman.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Martinus_Veltman.jpg/113px-Martinus_Veltman.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Martinus_Veltman.jpg/150px-Martinus_Veltman.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μάρτινους Τ.Τ. Φέλτμαν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9F%CE%BB%CE%BB%CE%B1%CE%BD%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ολλανδία"><img alt="Flag of the Netherlands.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/23px-Flag_of_the_Netherlands.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/35px-Flag_of_the_Netherlands.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/45px-Flag_of_the_Netherlands.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ολλανδία</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2000</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Zhores_Alferov.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Zhores Alferov.jpg" data-file-height="246" data-file-width="177" height="104" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/de/Zhores_Alferov.jpg/75px-Zhores_Alferov.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Zhores_Alferov.jpg/113px-Zhores_Alferov.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Zhores_Alferov.jpg/150px-Zhores_Alferov.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ζόρες Ιβάνοβιτς Αλφέροφ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A1%CF%89%CF%83%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ρωσία"><img alt="Flag of Russia.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/23px-Flag_of_Russia.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/35px-Flag_of_Russia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/45px-Flag_of_Russia.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ρωσία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανάπτυξη των ετεροδομών των ημιαγωγών που χρησιμοποιούνται σε υψηλές ταχύτητες και στην οπτικοηλεκτρονική»</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χέρμπερτ Κρέμερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζακ Κίλμπυ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμμετοχή του στην εφεύρεση του ολοκληρωμένου κυκλώματος»</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2001</span></td><td rowspan="2"></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Έρικ Άλιν Κόρνελ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για το επίτευγμα της συμπύκνωσης Bose-Einstein σε αέρια νέφη αλκακικών ατόμων, και για τις πρώιμες θεμελιώδεις μελέτες τους επί των ιδιοτήτων της συμπύκνωσης»</span></td></tr>
<tr><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Καρλ Έντουιν Βίμαν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Ketterle.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Ketterle.jpg" data-file-height="2000" data-file-width="1484" height="101" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Ketterle.jpg/75px-Ketterle.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Ketterle.jpg/113px-Ketterle.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Ketterle.jpg/150px-Ketterle.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Βόλφγκανγκ Κέτερλε</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2002</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ρέιμοντ Ντέιβις</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την πρωτότυπη συμβολή τους στην αστροφυσική, ειδικότερα στην ανίχνευση των κοσμικών νετρίνων»</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μασατόσι Κοσίμπα</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B1%CF%80%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιαπωνία"><img alt="Flag of Japan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/23px-Flag_of_Japan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/35px-Flag_of_Japan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/45px-Flag_of_Japan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιαπωνία</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:RiccardoGiacconi.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="RiccardoGiacconi.jpg" data-file-height="1655" data-file-width="1315" height="94" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/03/RiccardoGiacconi.jpg/75px-RiccardoGiacconi.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/RiccardoGiacconi.jpg/113px-RiccardoGiacconi.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/RiccardoGiacconi.jpg/150px-RiccardoGiacconi.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ρικάρντο Τζιακόνι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την πρωτότυπη συμβολή του στην αστροφυσική, η οποία οδήγησε στην ανακάλυψη των πηγών των κοσμικών ακτίνων Χ»</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2003</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:AA_Abrikosov_ANL1.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="AA Abrikosov ANL1.jpg" data-file-height="397" data-file-width="292" height="102" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0e/AA_Abrikosov_ANL1.jpg/75px-AA_Abrikosov_ANL1.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/AA_Abrikosov_ANL1.jpg/113px-AA_Abrikosov_ANL1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/AA_Abrikosov_ANL1.jpg/150px-AA_Abrikosov_ANL1.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Αλεξέι Αλεξέγιεβιτς Αμπρικόσοφ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A1%CF%89%CF%83%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ρωσία"><img alt="Flag of Russia.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/23px-Flag_of_Russia.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/35px-Flag_of_Russia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/45px-Flag_of_Russia.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ρωσία<br />Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την πρωτότυπη συμβολή τους στη θεωρία των ημιαγωγών και των υπερρευστών»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Ginzburg_in_MSU_opaque.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Ginzburg in MSU opaque.jpg" data-file-height="592" data-file-width="428" height="104" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Ginzburg_in_MSU_opaque.jpg/75px-Ginzburg_in_MSU_opaque.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Ginzburg_in_MSU_opaque.jpg/113px-Ginzburg_in_MSU_opaque.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Ginzburg_in_MSU_opaque.jpg/150px-Ginzburg_in_MSU_opaque.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Βίταλι Λαζάρεβιτς Γκίνσμπουργκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A1%CF%89%CF%83%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ρωσία"><img alt="Flag of Russia.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/23px-Flag_of_Russia.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/35px-Flag_of_Russia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/45px-Flag_of_Russia.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ρωσία</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Άντονι Τζέιμς Λέγκετ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α<br /><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2004</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:David_Gross_cropped.JPG" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="David Gross cropped.JPG" data-file-height="437" data-file-width="288" height="114" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/21/David_Gross_cropped.JPG/75px-David_Gross_cropped.JPG" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/David_Gross_cropped.JPG/113px-David_Gross_cropped.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/David_Gross_cropped.JPG/150px-David_Gross_cropped.JPG 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ντέιβιντ Γκρος</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της ασυμπτωτικής ελευθερίας στη θεωρία των ισχυρών αλληλεπιδράσεων»</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ντέιβιντ Πόλιτζερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:FrankStockholm2004.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="FrankStockholm2004.jpg" data-file-height="982" data-file-width="860" height="86" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b1/FrankStockholm2004.jpg/75px-FrankStockholm2004.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/FrankStockholm2004.jpg/113px-FrankStockholm2004.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/FrankStockholm2004.jpg/150px-FrankStockholm2004.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Φρανκ Γουίλτσεκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2005</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Roy_Glauber_Dec_10_2005.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Roy Glauber Dec 10 2005.jpg" data-file-height="466" data-file-width="410" height="85" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/75/Roy_Glauber_Dec_10_2005.jpg/75px-Roy_Glauber_Dec_10_2005.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Roy_Glauber_Dec_10_2005.jpg/113px-Roy_Glauber_Dec_10_2005.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Roy_Glauber_Dec_10_2005.jpg/150px-Roy_Glauber_Dec_10_2005.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ρόυ Τζ. Γκλάουμπερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συνεισφορά του στην κβαντική θεωρία οπτικής συμφωνίας»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:John_L._Hall.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="John L. Hall.jpg" data-file-height="267" data-file-width="200" height="100" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4f/John_L._Hall.jpg/75px-John_L._Hall.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/John_L._Hall.jpg/113px-John_L._Hall.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4f/John_L._Hall.jpg/150px-John_L._Hall.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζον Λ. Χολ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη συμβολή τους στην ανάπτυξη της φασματοσκοπίας ακριβείας βασισμένης σε λέιζερ, συμπεριλαμβανομένης της τεχνικής συνδυασμού οπτικών συχνοτήτων (optical frequency comb technique)»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Theodor_W_Haensch.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Theodor W Haensch.jpg" data-file-height="1026" data-file-width="1470" height="52" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/64/Theodor_W_Haensch.jpg/75px-Theodor_W_Haensch.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Theodor_W_Haensch.jpg/113px-Theodor_W_Haensch.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Theodor_W_Haensch.jpg/150px-Theodor_W_Haensch.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τέοντορ Β. Χενς</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2006</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:John-C-Mather.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="John-C-Mather.jpg" data-file-height="602" data-file-width="400" height="113" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/88/John-C-Mather.jpg/75px-John-C-Mather.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/John-C-Mather.jpg/113px-John-C-Mather.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/John-C-Mather.jpg/150px-John-C-Mather.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζον Μέιδερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της μορφής του μελανού σώματος και της ανισοτροπίας στην κοσμική ακτινοβολία μικροκυμάτων υποβάθρου»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:George_Smoot.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="George Smoot.jpg" data-file-height="1600" data-file-width="1200" height="100" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a8/George_Smoot.jpg/75px-George_Smoot.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/George_Smoot.jpg/113px-George_Smoot.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a8/George_Smoot.jpg/150px-George_Smoot.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζορτζ Σμουτ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2007</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Albert_Fert_at_EP2DS_2007_in_Genua_PICT5745.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Albert Fert at EP2DS 2007 in Genua PICT5745.jpg" data-file-height="1010" data-file-width="516" height="147" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Albert_Fert_at_EP2DS_2007_in_Genua_PICT5745.jpg/75px-Albert_Fert_at_EP2DS_2007_in_Genua_PICT5745.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Albert_Fert_at_EP2DS_2007_in_Genua_PICT5745.jpg/113px-Albert_Fert_at_EP2DS_2007_in_Genua_PICT5745.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Albert_Fert_at_EP2DS_2007_in_Genua_PICT5745.jpg/150px-Albert_Fert_at_EP2DS_2007_in_Genua_PICT5745.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Αλμπέρ Φερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη του φαινομένου της γιγάντιας μαγνητοαντίστασης (GRΜ)»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Peter_Gruenberg_01.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Peter Gruenberg 01.jpg" data-file-height="2900" data-file-width="2003" height="109" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Peter_Gruenberg_01.jpg/75px-Peter_Gruenberg_01.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Peter_Gruenberg_01.jpg/113px-Peter_Gruenberg_01.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Peter_Gruenberg_01.jpg/150px-Peter_Gruenberg_01.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πέτερ Γκρίνμπεργκ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%81%CE%BC%CE%B1%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γερμανία"><img alt="Flag of Germany.svg" class="thumbborder" data-file-height="600" data-file-width="1000" height="14" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/23px-Flag_of_Germany.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/35px-Flag_of_Germany.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Flag_of_Germany.svg/46px-Flag_of_Germany.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γερμανία</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2008</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Mkobayashi.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Mkobayashi.jpg" data-file-height="270" data-file-width="200" height="101" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/84/Mkobayashi.jpg/75px-Mkobayashi.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Mkobayashi.jpg/113px-Mkobayashi.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/84/Mkobayashi.jpg/150px-Mkobayashi.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μακότο Κομπαγιάσι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B1%CF%80%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιαπωνία"><img alt="Flag of Japan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/23px-Flag_of_Japan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/35px-Flag_of_Japan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/45px-Flag_of_Japan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιαπωνία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της προέλευσης της σπασμένης συμμετρίας, η οποία προβλέπει την ύπαρξη στη φύση τουλάχιστον τριών οικογενειών από κουάρκς»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Masukawa.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Masukawa.jpg" data-file-height="326" data-file-width="318" height="77" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/03/Masukawa.jpg/75px-Masukawa.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Masukawa.jpg/113px-Masukawa.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Masukawa.jpg/150px-Masukawa.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τοσιχίντε Μασκάουα</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B1%CF%80%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιαπωνία"><img alt="Flag of Japan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/23px-Flag_of_Japan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/35px-Flag_of_Japan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/45px-Flag_of_Japan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιαπωνία</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:YoichiroNambu.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="YoichiroNambu.jpg" data-file-height="1263" data-file-width="1082" height="88" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/YoichiroNambu.jpg/75px-YoichiroNambu.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/YoichiroNambu.jpg/113px-YoichiroNambu.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/YoichiroNambu.jpg/150px-YoichiroNambu.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γιοϊσίρο Νάμπου</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B1%CF%80%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιαπωνία"><img alt="Flag of Japan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/23px-Flag_of_Japan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/35px-Flag_of_Japan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/45px-Flag_of_Japan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιαπωνία</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη του μηχανισμού της αυτογενούς σπασμένης συμμετρίας στην υποατομική φυσική»</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2009</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Charles_K._Kao_cropped_2.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Charles K. Kao cropped 2.jpg" data-file-height="2350" data-file-width="2000" height="88" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Charles_K._Kao_cropped_2.jpg/75px-Charles_K._Kao_cropped_2.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Charles_K._Kao_cropped_2.jpg/113px-Charles_K._Kao_cropped_2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Charles_K._Kao_cropped_2.jpg/150px-Charles_K._Kao_cropped_2.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τσαρλς Κάο</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A7%CE%BF%CE%BD%CE%B3%CE%BA_%CE%9A%CE%BF%CE%BD%CE%B3%CE%BA" style="background: none; color: #0b0080;" title="Χονγκ Κονγκ"><img alt="Flag of Hong Kong.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Flag_of_Hong_Kong.svg/23px-Flag_of_Hong_Kong.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Flag_of_Hong_Kong.svg/35px-Flag_of_Hong_Kong.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Flag_of_Hong_Kong.svg/45px-Flag_of_Hong_Kong.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Χονγκ Κονγκ<br /><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αγγλία<br /><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τα επιτεύγματα σχετικά με τη μετάδοση του φωτός σε ίνες για την οπτική επικοινωνία»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Nobel_Prize_2009-Press_Conference_KVA-23.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Nobel Prize 2009-Press Conference KVA-23.jpg" data-file-height="2696" data-file-width="1858" height="109" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Nobel_Prize_2009-Press_Conference_KVA-23.jpg/75px-Nobel_Prize_2009-Press_Conference_KVA-23.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Nobel_Prize_2009-Press_Conference_KVA-23.jpg/113px-Nobel_Prize_2009-Press_Conference_KVA-23.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Nobel_Prize_2009-Press_Conference_KVA-23.jpg/150px-Nobel_Prize_2009-Press_Conference_KVA-23.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Γουίλαρντ Μπόυλ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%B1%CE%BD%CE%B1%CE%B4%CE%AC%CF%82" style="background: none; color: #0b0080;" title="Καναδάς"><img alt="Flag of Canada.svg" class="thumbborder" data-file-height="500" data-file-width="1000" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/23px-Flag_of_Canada.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/35px-Flag_of_Canada.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/46px-Flag_of_Canada.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Καναδάς<br /><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την εφεύρεση ενός κυκλώματος ημιαγωγών απεικόνισης - τον αισθητήρα CCD»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Nobel_Prize_2009-Press_Conference_KVA-24.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Nobel Prize 2009-Press Conference KVA-24.jpg" data-file-height="1688" data-file-width="2403" height="53" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Nobel_Prize_2009-Press_Conference_KVA-24.jpg/75px-Nobel_Prize_2009-Press_Conference_KVA-24.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Nobel_Prize_2009-Press_Conference_KVA-24.jpg/113px-Nobel_Prize_2009-Press_Conference_KVA-24.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Nobel_Prize_2009-Press_Conference_KVA-24.jpg/150px-Nobel_Prize_2009-Press_Conference_KVA-24.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζορτζ Σμιθ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2010</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Geim.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Geim.jpg" data-file-height="454" data-file-width="310" height="110" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/72/Geim.jpg/75px-Geim.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Geim.jpg/113px-Geim.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Geim.jpg/150px-Geim.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Αντρέ Γκέιμ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A1%CF%89%CF%83%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ρωσία"><img alt="Flag of Russia.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/23px-Flag_of_Russia.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/35px-Flag_of_Russia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/45px-Flag_of_Russia.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ρωσία<br /><a href="https://el.wikipedia.org/wiki/%CE%9F%CE%BB%CE%BB%CE%B1%CE%BD%CE%B4%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ολλανδία"><img alt="Flag of the Netherlands.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/23px-Flag_of_the_Netherlands.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/35px-Flag_of_the_Netherlands.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Flag_of_the_Netherlands.svg/45px-Flag_of_the_Netherlands.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ολλανδία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τα επαναστατικά τους πειράματα που αφορούν το δισδιάστατο υλικό γραφένιο»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Konstantin_Novoselov_at_MIPT.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Konstantin Novoselov at MIPT.jpg" data-file-height="1683" data-file-width="1122" height="113" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Konstantin_Novoselov_at_MIPT.jpg/75px-Konstantin_Novoselov_at_MIPT.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Konstantin_Novoselov_at_MIPT.jpg/113px-Konstantin_Novoselov_at_MIPT.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Konstantin_Novoselov_at_MIPT.jpg/150px-Konstantin_Novoselov_at_MIPT.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Κονσταντίν Νοβοσέλοφ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%A1%CF%89%CF%83%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ρωσία"><img alt="Flag of Russia.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/23px-Flag_of_Russia.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/35px-Flag_of_Russia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Flag_of_Russia.svg/45px-Flag_of_Russia.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ρωσία<br /><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ηνωμένο Βασίλειο</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2011</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Saul_Perlmutter.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Saul Perlmutter.jpg" data-file-height="334" data-file-width="198" height="127" src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/72/Saul_Perlmutter.jpg/75px-Saul_Perlmutter.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Saul_Perlmutter.jpg/113px-Saul_Perlmutter.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Saul_Perlmutter.jpg/150px-Saul_Perlmutter.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σαμ Περλμάτερ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της επιταχυνόμενης διαστολής του Σύμπαντος από παρατηρήσεις των μακρινών υπερκαινοφανών»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Brian_P_Schmidt.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Brian P Schmidt.jpg" data-file-height="260" data-file-width="192" height="102" src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/54/Brian_P_Schmidt.jpg/75px-Brian_P_Schmidt.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Brian_P_Schmidt.jpg/113px-Brian_P_Schmidt.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Brian_P_Schmidt.jpg/150px-Brian_P_Schmidt.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μπράιαν Σμιντ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%85%CF%83%CF%84%CF%81%CE%B1%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Αυστραλία"><img alt="Flag of Australia.svg" class="thumbborder" data-file-height="640" data-file-width="1280" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Flag_of_Australia.svg/23px-Flag_of_Australia.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Flag_of_Australia.svg/35px-Flag_of_Australia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Flag_of_Australia.svg/46px-Flag_of_Australia.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Αυστραλία<br /><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Adam_Riess.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Adam Riess.jpg" data-file-height="265" data-file-width="178" height="112" src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/01/Adam_Riess.jpg/75px-Adam_Riess.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Adam_Riess.jpg/113px-Adam_Riess.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Adam_Riess.jpg/150px-Adam_Riess.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Άνταμ Ρις</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2012</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Serge_Haroche_-_Th%C3%A9%C3%A2tre_de_la_Commune_d%27Aubervilliers_-_4_mai_2009.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Serge Haroche - Théâtre de la Commune d'Aubervilliers - 4 mai 2009.jpg" data-file-height="437" data-file-width="369" height="89" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Serge_Haroche_-_Th%C3%A9%C3%A2tre_de_la_Commune_d%27Aubervilliers_-_4_mai_2009.jpg/75px-Serge_Haroche_-_Th%C3%A9%C3%A2tre_de_la_Commune_d%27Aubervilliers_-_4_mai_2009.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Serge_Haroche_-_Th%C3%A9%C3%A2tre_de_la_Commune_d%27Aubervilliers_-_4_mai_2009.jpg/113px-Serge_Haroche_-_Th%C3%A9%C3%A2tre_de_la_Commune_d%27Aubervilliers_-_4_mai_2009.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Serge_Haroche_-_Th%C3%A9%C3%A2tre_de_la_Commune_d%27Aubervilliers_-_4_mai_2009.jpg/150px-Serge_Haroche_-_Th%C3%A9%C3%A2tre_de_la_Commune_d%27Aubervilliers_-_4_mai_2009.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σερζ Αρός</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις επαναστατικές πειραματικές μεθόδους που επιτρέπουν τη μέτρηση και το χειρισμό μεμονωμένων κβαντικών συστημάτων»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:David_Wineland_2008crop.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="David Wineland 2008crop.jpg" data-file-height="681" data-file-width="596" height="86" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/af/David_Wineland_2008crop.jpg/75px-David_Wineland_2008crop.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/David_Wineland_2008crop.jpg/113px-David_Wineland_2008crop.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/af/David_Wineland_2008crop.jpg/150px-David_Wineland_2008crop.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ντέιβιντ Γουάινλαντ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2013</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Higgs,_Peter_(1929)3.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Higgs, Peter (1929)3.jpg" data-file-height="375" data-file-width="250" height="113" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Higgs%2C_Peter_%281929%293.jpg/75px-Higgs%2C_Peter_%281929%293.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Higgs%2C_Peter_%281929%293.jpg/113px-Higgs%2C_Peter_%281929%293.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Higgs%2C_Peter_%281929%293.jpg/150px-Higgs%2C_Peter_%281929%293.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Πίτερ Χιγκς</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ηνωμένο Βασίλειο</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τη θεωρητική ανακάλυψη του μηχανισμού που συνεισφέρει στην κατανόησή μας για την προέλευση της μάζας των υποατομικών σωματιδίων, ο οποίος πρόσφατα επιβεβαιώθηκε με την ανακάλυψη του προβλεπόμενου στοιχειώδους σωματιδίου, από τα πειράματα ATLAS και CMS του επιταχυντή LHC του CERΝ»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Francois_Englert.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Francois Englert.jpg" data-file-height="1082" data-file-width="808" height="100" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Francois_Englert.jpg/75px-Francois_Englert.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Francois_Englert.jpg/113px-Francois_Englert.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Francois_Englert.jpg/150px-Francois_Englert.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Φρανσουά Ανγκλέρ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%92%CE%AD%CE%BB%CE%B3%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Βέλγιο"><img alt="Flag of Belgium.svg" class="thumbborder" data-file-height="390" data-file-width="450" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/65/Flag_of_Belgium.svg/17px-Flag_of_Belgium.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Flag_of_Belgium.svg/27px-Flag_of_Belgium.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Flag_of_Belgium.svg/35px-Flag_of_Belgium.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="17" /></a> Βέλγιο</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2014</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ισάμου Ακαζάκι</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B1%CF%80%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιαπωνία"><img alt="Flag of Japan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/23px-Flag_of_Japan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/35px-Flag_of_Japan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/45px-Flag_of_Japan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιαπωνία</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη φωτοδιόδων μπλε χρώματος που επιτρέπει την έκλυση λαμπρού φωτός από ενεργειακά οικονομικές πηγές φωτός.»</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Χιρόσι Αμάνο</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B1%CF%80%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιαπωνία"><img alt="Flag of Japan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/23px-Flag_of_Japan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/35px-Flag_of_Japan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/45px-Flag_of_Japan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιαπωνία</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Professor_Shuji_Nakamura_(Cropped).jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Professor Shuji Nakamura (Cropped).jpg" data-file-height="1052" data-file-width="1126" height="70" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Professor_Shuji_Nakamura_%28Cropped%29.jpg/75px-Professor_Shuji_Nakamura_%28Cropped%29.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Professor_Shuji_Nakamura_%28Cropped%29.jpg/113px-Professor_Shuji_Nakamura_%28Cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Professor_Shuji_Nakamura_%28Cropped%29.jpg/150px-Professor_Shuji_Nakamura_%28Cropped%29.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Σούτζι Νακαμούρα</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B1%CF%80%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιαπωνία"><img alt="Flag of Japan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/23px-Flag_of_Japan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/35px-Flag_of_Japan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/45px-Flag_of_Japan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιαπωνία<br /><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2015</span></td><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Takaaki_Kajita_5171-2015.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Takaaki Kajita 5171-2015.jpg" data-file-height="2705" data-file-width="2705" height="75" src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/23/Takaaki_Kajita_5171-2015.jpg/75px-Takaaki_Kajita_5171-2015.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Takaaki_Kajita_5171-2015.jpg/113px-Takaaki_Kajita_5171-2015.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Takaaki_Kajita_5171-2015.jpg/150px-Takaaki_Kajita_5171-2015.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τακάκι Κατζίτα</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B1%CF%80%CF%89%CE%BD%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Ιαπωνία"><img alt="Flag of Japan.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/23px-Flag_of_Japan.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/35px-Flag_of_Japan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Flag_of_Japan.svg/45px-Flag_of_Japan.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ιαπωνία</span></td><td rowspan="2"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για την ανακάλυψη της ταλάντωσης των νετρίνων, η οποία δείχνει ότι τα νετρίνα έχουν μάζα.»</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:Arthur_B._McDonald_5193-2015.jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Arthur B. McDonald 5193-2015.jpg" data-file-height="3204" data-file-width="2748" height="87" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Arthur_B._McDonald_5193-2015.jpg/75px-Arthur_B._McDonald_5193-2015.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Arthur_B._McDonald_5193-2015.jpg/113px-Arthur_B._McDonald_5193-2015.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Arthur_B._McDonald_5193-2015.jpg/150px-Arthur_B._McDonald_5193-2015.jpg 2x" style="border: 0px; vertical-align: middle;" width="75" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Άρθουρ Μπ. Μακντόναλντ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%B1%CE%BD%CE%B1%CE%B4%CE%AC%CF%82" style="background: none; color: #0b0080;" title="Καναδάς"><img alt="Flag of Canada.svg" class="thumbborder" data-file-height="500" data-file-width="1000" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/23px-Flag_of_Canada.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/35px-Flag_of_Canada.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/46px-Flag_of_Canada.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Καναδάς</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2016</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ντέιβιντ Θούλες</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ηνωμένο Βασίλειο<br /><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για θεωρητικές ανακαλύψεις τοπολογικών μεταβάσεων φάσης και τοπολογικών φάσεων της ύλης».</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ντάνκαν Χάλντεϊν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ηνωμένο Βασίλειο<br /><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Τζον Μ. Κόστερλιτς</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%BF_%CE%92%CE%B1%CF%83%CE%AF%CE%BB%CE%B5%CE%B9%CE%BF" style="background: none; color: #0b0080;" title="Ηνωμένο Βασίλειο"><img alt="Flag of the United Kingdom.svg" class="thumbborder" data-file-height="600" data-file-width="1200" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/23px-Flag_of_the_United_Kingdom.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/35px-Flag_of_the_United_Kingdom.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Flag_of_the_United_Kingdom.svg/46px-Flag_of_the_United_Kingdom.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Ηνωμένο Βασίλειο</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2017</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ράινερ Βάις</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">«για τις αποφασιστικές τους συνεισφορές στον ανιχνευτή LIGO και την παρατήρηση βαρυτικών κυμάτων».</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Μπάρι Μπάρις</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Κιπ Θορν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td></tr>
<tr><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">2018</span></td><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Άρθουρ Άσκιν</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%97%CE%BD%CF%89%CE%BC%CE%AD%CE%BD%CE%B5%CF%82_%CE%A0%CE%BF%CE%BB%CE%B9%CF%84%CE%B5%CE%AF%CE%B5%CF%82_%CE%91%CE%BC%CE%B5%CF%81%CE%B9%CE%BA%CE%AE%CF%82" style="background: none; color: #0b0080;" title="Ηνωμένες Πολιτείες Αμερικής"><img alt="Flag of the United States.svg" class="thumbborder" data-file-height="650" data-file-width="1235" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/23px-Flag_of_the_United_States.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/35px-Flag_of_the_United_States.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Flag_of_the_United_States.svg/46px-Flag_of_the_United_States.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Η.Π.Α</span></td><td rowspan="3"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">"για τις καινοτόμες εφευρέσεις τους στον τομέα της φυσικής των λέιζερ"</span></td></tr>
<tr><td><a class="image" href="https://commons.wikimedia.org/wiki/File:G%C3%A9rard_Mourou_(cropped).jpg" style="background: none; color: #0b0080;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><img alt="Gérard Mourou (cropped).jpg" data-file-height="3183" data-file-width="3127" src="https://upload.wikimedia.org/wikipedia/commons/thumb/b/bd/G%C3%A9rard_Mourou_%28cropped%29.jpg/75px-G%C3%A9rard_Mourou_%28cropped%29.jpg" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/G%C3%A9rard_Mourou_%28cropped%29.jpg/113px-G%C3%A9rard_Mourou_%28cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bd/G%C3%A9rard_Mourou_%28cropped%29.jpg/150px-G%C3%A9rard_Mourou_%28cropped%29.jpg 2x" style="border: 0px; vertical-align: middle;" /></span></a></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ζεράρ Μουρού</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B1%CE%BB%CE%BB%CE%AF%CE%B1" style="background: none; color: #0b0080;" title="Γαλλία"><img alt="Flag of France.svg" class="thumbborder" data-file-height="600" data-file-width="900" height="15" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/23px-Flag_of_France.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/35px-Flag_of_France.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Flag_of_France.svg/45px-Flag_of_France.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Γαλλία</span></td><td></td></tr>
<tr><td></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;">Ντόνα Στρίκλαντ</span></td><td><span style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%B1%CE%BD%CE%B1%CE%B4%CE%AC%CF%82" style="background: none; color: #0b0080;" title="Καναδάς"><img alt="Flag of Canada.svg" class="thumbborder" data-file-height="500" data-file-width="1000" height="12" src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/23px-Flag_of_Canada.svg.png" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/35px-Flag_of_Canada.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Flag_of_Canada.svg/46px-Flag_of_Canada.svg.png 2x" style="border: 1px solid rgb(234, 236, 240); vertical-align: middle;" width="23" /></a> Καναδάς</span></td></tr>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-32440614457798351312018-11-15T12:34:00.000-08:002020-09-12T09:54:51.882-07:00ΙΣΤΟΡΙΑ ΤΗΣ ΠΑΡΑΤΗΡΗΣΗΣ ΤΟΥ ΑΡΗ<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="color: red; font-family: "verdana" , sans-serif; font-size: x-large;"><b>ΙΣΤΟΡΙΑ ΤΗΣ ΠΑΡΑΤΗΡΗΣΗΣ ΤΟΥ ΑΡΗ</b></span></div>
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<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: large;">ΙΣΤΟΡΙΑ ΤΗΣ ΠΑΡΑΤΗΡΗΣΗΣ ΤΟΥ ΑΡΗ</span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b>Η ιστορία των παρατηρήσεων του Άρη χαρακτηρίζεται από τις αντιθέσεις του Άρη,όταν ο πλανήτης είναι πιο κοντά στη Γη και ως εκ τούτου είναι πιο εύκολα ορατός γεγονός που γίνεται κάθε δύο χρόνια.</b>Ακόμη πιο αξιοσημείωτη είναι οι αντιθέσεις του <b>Άρη</b> που συμβαίνουν κάθε <b>15</b> ή <b>17</b> χρόνια,και διακρίνονται επειδή ο <b>Άρης</b> είναι κοντά στο περιήλιο.</span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px;"><b><span class="Apple-style-span" style="color: purple;"> Η ύπαρξη του Άρη ως αντικείμενο στον ουρανό της νύχτας καταγράφηκε από τους αρχαίους αιγυπτιακούς αστρονόμους από 1534 π.Χ. που ήταν εξοικειωμένοι με την ανάδρομη κίνηση του πλανήτη</span></b></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b>Η ύπαρξη του Άρη ως αντικείμενο στον ουρανό της νύχτας καταγράφηκε από τους αρχαίους αιγυπτιακούς αστρονόμους από 1534 π.Χ. που ήταν εξοικειωμένοι με την ανάδρομη κίνηση του πλανήτη.</b></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Με την περίοδο της <b>Νέο-Βαβυλωνιακής</b> αυτοκρατορίας,η βαβυλωνιακή αστρονόμοι πραγματοποιούσαν τακτικά αρχεία των θέσεων των πλανητών και τις συστηματικές παρατηρήσεις της συμπεριφοράς τους.Για τον<b> Άρη</b>, ήξεραν ότι ο πλανήτης είχε <b>37</b> συνοδική περίοδο,ή <b>42</b> κυκλώματα του ζωδιακού κύκλου,κάθε <b>79</b> χρόνια.</span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px;"><b><span class="Apple-style-span" style="color: purple;">Στο τέταρτο αιώνα π.Χ.,ο Αριστοτέλης σημειώνει ότι ο Άρης εξαφανίστηκε πίσω από το φεγγάρι κατά τη διάρκεια μιας απόκρυψης,που δείχνει ότι ο πλανήτης ήταν πιο μακριά</span></b></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Στο τέταρτο αιώνα<b> π.Χ.</b>,ο <b>Αριστοτέλης</b> σημειώνει ότι ο <b>Άρης</b> εξαφανίστηκε πίσω από το φεγγάρι κατά τη διάρκεια μιας απόκρυψης, που δείχνει ότι ο πλανήτης ήταν πιο μακριά.Ο <b>Πτολεμαίος</b>,ένας <b>Έλληνας </b>που ζούσε στην <b>Αλεξάνδρεια</b>,επιχείρησε να αντιμετωπίσει το πρόβλημα της τροχιακής κίνησης του <b>Άρη</b>.Το μοντέλο του <b>Πτολεμαίου</b> και τη συλλογική εργασία του σχετικά με την αστρονομία παρουσιάστηκε στη πολύτομη συλλογή <b>Αλμαγέστη</b>,η οποία έγινε η επίσημη πραγματεία για τη <b>Δυτική</b> αστρονομία για τους επόμενους δεκατέσσερις αιώνες.Η λογοτεχνία από την αρχαία <b>Κίνα</b> επιβεβαιώνει ότι ο <b>Άρης</b> ήταν γνωστός από τους <b>Κινέζους </b>αστρονόμους το αργότερο από τον τέταρτο αιώνα <b>π.Χ.</b>.Στον πέμπτο αιώνα <b>μ.Χ.</b>,το ινδικό αστρονομικό κείμενο <b>Surya Siddhanta</b> εκτιμάται η διάμετρος του <b>Άρη</b></span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">. </span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px;"><b><span class="Apple-style-span" style="color: purple;">Η λογοτεχνία από την αρχαία Κίνα επιβεβαιώνει ότι ο Άρης ήταν γνωστός από τους Κινέζους αστρονόμους το αργότερο από τον τέταρτο αιώνα π.Χ.</span></b></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Κατά τη διάρκεια του δέκατου έβδομου αιώνα,ο <b>Tycho Brahe</b> μετράει τη ημερήσια παράλλαξη του <b>Άρη</b> που ο <b>Johannes Kepler </b>χρησιμοποιεί για να κάνει υπολογισμό της σχετικής απόστασης του πλανήτη.Όταν το τηλεσκόπιο έγινε διαθέσιμο,η ημερήσια παράλλαξη του <b>Άρη</b> μετριέται σε μια προσπάθεια για τον καθορισμό της </span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;">απόστασης</span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b>Ήλιου-Γης</b>.Αυτή ήταν η πρώτη προσπάθεια από τον <b>Giovanni Domenico Cassini το 1672</b>.Οι πρώτες μετρήσεις παράλλαξης είχαν παρεμποδιστεί από την ποιότητα των οργάνων.Η μόνη απόκρυψη του <b>Άρη</b> από την <b>Αφροδίτη </b>που παρατηρήθηκε ήταν ότι της <b>13ης Οκτωβρίου 1590</b>.Το <b>1610</b>,ο <b>Άρης</b> θεωρήθηκε από το σύστημα <b>Galileo Galilei</b>,ο οποίος για πρώτη φορά τον παρατήρησε μέσω του τηλεσκοπίου.Ο πρώτος που σχεδίασε χάρτη του <b>Άρη</b>,ήταν ο<b> Ολλανδός </b>αστρονόμος <b>Christiaan Huygens</b>.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Μέχρι το<b> 19ο αιώνα</b>,η επίλυση των τηλεσκοπίων έχει φθάσει σε επίπεδο επαρκές για να τα χαρακτηριστικά της επιφάνειας.Το <b>1877</b> ο<b> Ιταλός</b> αστρονόμος <b>Giovanni Schiaparelli</b> χρησιμοποίησε ένα τηλεσκόπιο <b>22</b> εκατοστών στο <b>Μιλάνο</b> για να βοηθήσει στην παραγωγή του πρώτου ακριβή χάρτη του πλανήτη <b>Άρη</b>.</span><br />
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-8038095242979783592017-05-10T16:44:00.000-07:002020-09-12T09:54:52.077-07:00ΣΗΜΕΙΟ ΤΗΞΕΩΣ<div dir="ltr" style="text-align: left;" trbidi="on">
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<strong><span style="color: red; font-family: "verdana" , sans-serif;"><br /></span></strong><span style="color: red; font-family: "verdana" , sans-serif; font-weight: bold;"> </span><span style="font-family: "verdana" , sans-serif;">Ο πάγος γίνεται πάλι νερό,όταν παραμείνει έξω από την κατάψυξη,γιατί παίρνει θερμότητα από το περιβάλλον.Το φαινόμενο αυτό,κατά το οποίο ένα στερεό μετατρέπεται σε υγρό,λέγεται <b>τήξη.</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="color: red; font-family: "verdana" , sans-serif;"><b>ΟΡΙΣΜΟΣ ΤΗΞΕΩΣ</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><br /></b></span><span style="font-family: "verdana" , sans-serif;"> Ο πάγος γίνεται πάλι νερό,όταν παραμείνει έξω από την κατάψυξη,γιατί παίρνει θερμότητα από το περιβάλλον.Το φαινόμενο αυτό,κατά το οποίο ένα στερεό μετατρέπεται σε υγρό,λέγεται τήξη.</span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="color: purple; font-size: small;"><strong style="line-height: 16px; text-align: justify;"><span style="font-family: "verdana" , sans-serif;">Τήξη</span></strong><span style="font-family: "verdana" , sans-serif; line-height: 16px; text-align: justify;"><b> ονομάζεται το φαινόμενο της μετατροπής στερεού υλικού σε υγρό</b></span></span></td></tr>
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<strong><span style="font-family: "lucida grande" , "tahoma" , "verdana" , "arial" , sans-serif; font-size: 11px;"> </span><span style="color: blue; font-family: "verdana" , sans-serif;">Τήξη</span></strong><span style="font-family: "verdana" , sans-serif;"><b> ονομάζεται το φαινόμενο της μετατροπής στερεού υλικού σε υγρό.</b>Η Τήξη αποτελεί μια από τις αλλαγές φάσεων της φυσικής μορφής της ύλης.</span><span style="font-family: "verdana" , sans-serif;">Τα παράγωγα της τήξης καλούνται </span><strong style="font-family: Verdana, sans-serif;">τήγματα</strong><span style="font-family: "verdana" , sans-serif;">.</span><br />
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<b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Η τήξη του νερού σε ένα ποτήρι</span></b></div>
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<span style="font-family: "verdana" , sans-serif; text-align: center;"> Καθώς θερμαίνεται ένα στερεό τα σωματίδιά του που συγκροτούν αυτό αρχίζουν να ταλαντώνονται όλο και ταχύτερα.Έτσι σιγά σιγά υπερνικούν τις μεταξύ τους ελκτικές δυνάμεις που τα συγκρατούν στις πρότερες θέσεις ισορροπίας τους με αποτέλεσμα το στερεό να λιώνει.</span></div>
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<span style="font-family: "verdana" , sans-serif;"></span><span style="color: red; font-family: "verdana" , sans-serif;"><b>ΣΗΜΕΙΟ ΤΗΞΕΩΣ</b></span><br />
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<span style="font-family: "verdana" , sans-serif;"> Τοποθετούμε τριμμένα παγάκια σ' ένα δοχείο και μέσα σε αυτά βυθίζουμε ένα θερμόμετρο και το τοποθετούμε σε εστία θέρμανσης.Η θερμοκρασία του πάγου αρχίζει να αυξάνεται.Όταν φθάσει στους<b> 0 °C,</b>τότε ο πάγος αρχίζει να λιώνει,οπότε εμφανίζεται και νερό μέσα στο ποτήρι.Παρατηρούμε ότι μέχρι να λιώσει όλος ο πάγος,η θερμοκρασία του μείγματος νερού-πάγου διατηρείται σταθερή στους <b>0 °C.</b>Η θερμοκρασία αυτή ονομάζεται θερμοκρασία ή σημείο τήξης του πάγου.Μόλις λιώσει όλος ο πάγος,η θερμοκρασία του νερού αρχίζει να αυξάνεται.</span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><b>Σημείο τήξης ή θερμοκρασία τήξης ονομάζεται η θερμοκρασία στην οποία αλλάζει φάση μια καθαρή ουσία μεταβαίνοντας από την στερεά κατάσταση στην υγρή κατάσταση</b></span></td></tr>
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<strong><span style="font-family: "lucida grande" , "tahoma" , "verdana" , "arial" , sans-serif; font-size: 11px;"> </span><span style="color: blue; font-family: "verdana" , sans-serif;">Σημείο τήξης</span></strong><span style="font-family: "verdana" , sans-serif;"><b><span style="color: blue;"> ή θερμοκρασία τήξης</span> ονομάζεται η θερμοκρασία στην οποία αλλάζει φάση μια καθαρή ουσία μεταβαίνοντας από την στερεά κατάσταση στην υγρή κατάσταση</b>.Είναι η θερμοκρασία εκείνη στην οποία συνυπάρχουν σε ισορροπία τόσο η στερεά όσο και η υγρή κατάσταση μιας ουσίας.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b> </b>Για να μελετήσουμε πειραματικά την τήξη,χρησιμοποιούμε την συσκευή του παρακάτω σχήματος.Ο δοκιμαστικός σωλήνας περιέχει σκόνη ναφθαλίνης και βρίσκεται μέσα σε έναν άλλο σωλήνα που είναι βυθισμένος στο νερό του δοχείου.</span><br />
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<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Τήξη της ναφθαλίνης</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Όταν θερμαίνουμε τη συσκευή αυτή με τη φλόγα ενός λύχνου,η ναφθαλίνη θερμαίνεται αργά εξαιτίας του σωλήνα και του αέρα που περιέχει αυτός.Με το θερμόμετρο μετράμε τη θερμοκρασία της ναφθαλίνης.</span></div>
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<span style="font-family: "verdana" , sans-serif;"> Κατά τη διάρκεια της θερμάνσεως παρατηρούμε τα ακόλουθα:Στην αρχή η ναφθαλίνη είναι στερεή και η θερμοκρασία της μεγαλώνει σιγά σιγά.Όταν η θερμοκρασία της γίνει<b> 80 </b></span><span style="font-family: "verdana" , sans-serif;"><b>°C</b> αρχίζει η τήξη της.Η θερμοκρασία της ναφθαλίνης παραμένει σταθερή στους </span><span style="font-family: "verdana" , sans-serif;"><b>80 </b></span><span style="font-family: "verdana" , sans-serif;"><b>°C</b> σε όλη τη χρονική διάρκεια της τήξεως.Όταν τελειώσει η τήξη όλης της ναφθαλίνης,η θερμοκρασία της αυξάνεται πάλι σιγά σιγά.</span></div>
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<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="font-family: 'Times New Roman';"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Μεταβολή της θερμοκρασίας του σώματος σε συνάρτηση με το χρόνο κατά το πείραμα της τήξεως</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Αν κατά την διάρκεια του πειράματος μετράμε τη θερμοκρασία π.χ. κάθε <b>1 min,</b>μπορούμε να κατασκευάσουμε το διάγραμμα της θερμοκρασίας με το χρόνο του παραπάνω σχήματος.</span></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-27798060692928099722017-01-04T16:35:00.001-08:002020-09-12T09:54:52.273-07:00ΣΗΜΕΙΟ ΠΗΞΗΣ<div dir="ltr" style="text-align: left;" trbidi="on">
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<b style="color: red; font-family: Verdana, sans-serif;"><span style="font-size: x-large;">ΣΗΜΕΙΟ ΠΗΞΗΣ</span></b><br />
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<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-family: Verdana, sans-serif; font-size: large;">ΣΗΜΕΙΟ ΠΗΞΗΣ</span></b></td></tr>
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<span style="color: red; font-family: "verdana" , sans-serif;"><b>ΕΙΣΑΓΩΓΗ</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"> Το νερό που βάζουμε στην κατάψυξη του ψυγείου μας γίνεται πάγος γιατί χάνει θερμότητα.</span></div>
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<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">Το νερό που βάζουμε στην κατάψυξη του ψυγείου μας γίνεται πάγος γιατί χάνει θερμότητα</span></span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Το φαινόμενο αυτό,κατά το οποίο ένα υγρό μετατρέπεται σε στερεό,λέγεται <b>πήξη.</b></span></div>
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<span style="color: red; font-family: "verdana" , sans-serif;"><b>ΟΡΙΣΜΟΣ ΠΗΞΗΣ</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><strong> <span style="color: blue;">Πήξη</span></strong><b><span style="color: blue;"> </span>ονομάζεται το φαινόμενο της μετατροπής ενός υγρού σε στερεό.</b></span><br />
<span style="font-family: "verdana" , sans-serif;"> Η πήξη αποτελεί μια από τις αλλαγές φάσεων της φυσικής μορφής της ύλης.</span></div>
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<span style="font-family: "verdana" , sans-serif;"> Όταν ψύχεται ένα υγρό,οι δυνάμεις μεταξύ των σωματιδίων που το συγκροτούν,γίνονται όλο και πιο ισχυρές καθώς μειώνεται η κίνησή των μορίων έτσι ώστε στο τέλος το υγρό στερεοποιείται.</span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="color: purple; font-size: small;"><strong style="font-family: Verdana, sans-serif; line-height: 16px; text-align: justify;">Πήξη</strong><b style="font-family: Verdana, sans-serif; line-height: 16px; text-align: justify;"> ονομάζεται το φαινόμενο της μετατροπής ενός υγρού σε στερεό</b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Τοποθετούμε ένα δοχείο με νερό μέσα σε μια λεκάνη με πάγο θερμοκρασίας <b>-10 °C.</b>Παρατηρούμε ότι η θερμοκρασία του νερού μειώνεται.Όταν φθάσει στους <b>0 °C,</b>το νερό αρχίζει να γίνεται στερεό,δηλαδή πάγος.Αυτή η θερμοκρασία διατηρείται σταθερή μέχρι να γίνει πάγος όλο το νερό.Την ονομάζουμε <b>θερμοκρασία πήξης του νερού.</b></span></div>
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<b style="font-family: Verdana, sans-serif;"><span style="color: red;">ΣΗΜΕΙΟ ΠΗΞΗΣ</span></b></div>
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<span style="font-family: "verdana" , sans-serif;"><strong style="text-align: -webkit-auto;"> <span style="color: blue;">Σημείο </span><span style="color: blue;">ή </span><span style="color: blue;">θερμοκρασία πήξης</span></strong><span style="text-align: -webkit-auto;"><b> ονομάζεται η θερμοκρασία κατά την οποία ένα σώμα περνά από την υγρή κατάσταση σε στερεή.</b></span></span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimpSKeErWwhgQ22jQldJcsjTywaUoAERIzJSlPF7w2pQBMZi40nfGCaZ9b8IXGO7kDx94og3bbYEvZlfN30opm0BnEkNwcZ0pnEPWw1frPSsBpLv-ZYwHL5CSrbbLT3igWmFRMWFU0AKM6/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(35).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimpSKeErWwhgQ22jQldJcsjTywaUoAERIzJSlPF7w2pQBMZi40nfGCaZ9b8IXGO7kDx94og3bbYEvZlfN30opm0BnEkNwcZ0pnEPWw1frPSsBpLv-ZYwHL5CSrbbLT3igWmFRMWFU0AKM6/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(35).JPG" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><strong style="line-height: 16px; text-align: -webkit-auto;">Σημείο ή θερμοκρασία πήξης</strong><span style="font-family: "verdana" , sans-serif; line-height: 16px;"><b> ονομάζεται η θερμοκρασία κατά την οποία ένα σώμα περνά από την υγρή κατάσταση σε στερεή.</b></span></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"><b> </b>Για να μελετήσουμε πειραματικά την πήξη,βάζουμε το σύστημα των σωλήνων με την υγρή ναφθαλίνη μέσα στο ψυχρό νερό.Κατά τη διάρκεια της ψύξεως παρατηρούμε τα εξής:Στην αρχή η ναφθαλίνη είναι υγρή και η θερμοκρασία της ελαττώνεται προοδευτικά ώσπου να γίνει<b> </b></span><span style="font-family: "verdana" , sans-serif;"><b>80 </b></span><span style="font-family: "verdana" , sans-serif;"><b>°C ,</b>οπότε αρχίζει η πήξη της.Σε όλη τη χρονική διάρκεια της πήξεως η θερμοκρασία παραμένει σταθερή <b>(</b></span><span style="font-family: "verdana" , sans-serif;"><b>80 </b></span><span style="font-family: "verdana" , sans-serif;"><b>°C),</b>ώσπου να γίνει όλη η ναφθαλίνη στερεή.Κατόπιν η θερμοκρασία αρχίζει και πάλι να ελαττώνεται </span><span style="font-family: "verdana" , sans-serif;"> προοδευτικά.</span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS-1pb_jANoJLGvIITQ5szVFToeDwEobwmUtiixMOLIYI43SZpP6Se83xSp1Yp6p-DfL_IASddQBc0OetVtr027cxR_90TZIshl6ljaw40eAR98THxgLY5DWUHMl_9M5Yf3CRfVhv9yxc/s1600/%CE%95%CE%9E%CE%91%CE%93%CE%9D%CE%A9%CE%A3%CE%97(4).jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="356" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS-1pb_jANoJLGvIITQ5szVFToeDwEobwmUtiixMOLIYI43SZpP6Se83xSp1Yp6p-DfL_IASddQBc0OetVtr027cxR_90TZIshl6ljaw40eAR98THxgLY5DWUHMl_9M5Yf3CRfVhv9yxc/s400/%CE%95%CE%9E%CE%91%CE%93%CE%9D%CE%A9%CE%A3%CE%97(4).jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Μεταβολή της θερμοκρασίας του σώματος σε συνάρτηση με το χρόνο κατά το πείραμα της πήξεως</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Η μεταβολή αυτής της θερμοκρασίας της ναφθαλίνης,σε συνάρτηση με το χρόνο,φαίνεται στο παραπάνω διάγραμμα.</span></div>
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<span style="font-family: "verdana" , sans-serif;"> </span><span style="font-family: "verdana" , sans-serif;">Η πήξη ειδικά στη μεταλλουργία αποτελεί μείζονος σημασίας στάδιο τόσο στη διαδικασία της χύτευσης όσο και της συγκόλλησης μετάλλων και κραμάτων όπου παρεμβαίνουν πολλοί παράμετροι στη διαδικασία του μετασχηματισμού τους, όπως π.χ. μεταβολή του όγκου τους,η ανακατανομή των δομικών μονάδων τους κ.λπ.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="color: red; font-family: "verdana" , sans-serif;"><b>ΝΟΜΟΙ ΤΗΞΕΩΣ-ΠΗΞΕΩΣ</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><br /></b></span><span style="font-family: "verdana" , sans-serif;"><b> </b>Από τα πειράματα που αναφέραμε μπορούμε να βγάλουμε τα παρακάτω συμπεράσματα που αποτελούν τους νόμους της τήξεως και της πήξεως.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">α)</span> Όταν η πίεση είναι σταθερή,η τήξη(ή η πήξη) ενός σώματος αρχίζει σε ορισμένη θερμοκρασία,που είναι χαρακτηριστική για κάθε σώμα και λέγεται θερμοκρασία ή σημείο τήξεως (ή πήξεως).</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">β)</span> Όσο διαρκεί η τήξη(ή η πήξη),η θερμοκρασία παραμένει σταθερή και ίση με το σημείο τήξεως(ή πήξεως)</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">γ) </span>Όσο διαρκεί η τήξη(ή η πήξη) συνυπάρχουν η υγρή και στερεή κατάσταση του σώματος.</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">δ)</span> Για ένα ορισμένο σώμα η θερμοκρασία τήξεως είναι ίδια με την θερμοκρασία πήξεως.</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">ε) </span>Η θερμοκρασία τήξης (ή πήξεως) εξαρτάται από το υλικό του σώματος.</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">στ)</span> Ο όγκος του σώματος,κατά την διάρκεια του φαινομένου τήξης(ή πήξεως),αλλάζει.</b></span></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-51627665727250685242016-12-15T18:33:00.000-08:002020-09-12T09:54:52.469-07:00ΦΩΤΕΙΝΗ ΕΝΕΡΓΕΙΑ<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="color: red; font-family: Verdana, sans-serif; line-height: 16px; text-align: justify;"><span style="font-size: x-large;">ΦΩΤΕΙΝΗ ΕΝΕΡΓΕΙΑ</span></b><br />
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<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: large;">ΦΩΤΕΙΝΗ ΕΝΕΡΓΕΙΑ</span></b></td></tr>
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<span style="color: red; font-family: "verdana" , sans-serif;"><strong>ΕΙΣΑΓΩΓΗ</strong></span><br />
<span style="font-family: "verdana" , sans-serif;"><strong><br /></strong></span><span style="font-family: "verdana" , sans-serif;"><strong> <span style="color: blue;">Φωτεινή ενέργεια </span>ονομάζεται η</strong><b> ενέργεια που μεταφέρει το φως η οποία αποτελεί ειδική περίπτωση της ενέργειας ακτινοβολίας</b>.Έτσι η φωτεινή ενέργεια όπως και κάθε μορφή ενέργειας είναι δυνατό να μετασχηματιστεί σε άλλες μορφές.<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
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<tr><td class="tr-caption" style="text-align: center;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><strong style="text-align: justify;">Φωτεινή ενέργεια ονομάζεται η</strong><b style="text-align: justify;"> ενέργεια που μεταφέρει το φως η οποία αποτελεί ειδική περίπτωση της ενέργειας ακτινοβολίας</b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> <span style="text-align: -webkit-auto;"><b>Φωτεινή ενέργεια</b></span><span style="text-align: -webkit-auto;"> χαρακτηρίζεται εκείνη η ενέργεια της οποίας δημιουργείται η αίσθηση της όρασης,δηλαδή η ενέργεια που γίνεται ορατή από το ανθρώπινο μάτι.</span><span style="text-align: -webkit-auto;">Οι λαμπτήρες και οι φακοί μετατρέπουν την ηλεκτρική ενέργεια ή θερμική ενέργεια σε φως.</span></span><br />
<span style="font-family: "verdana" , sans-serif;"><span style="text-align: -webkit-auto;"> Οι δε φωτεινές ακτίνες,υπό μορφή ηλεκτρομαγνητικής ακτινοβολίας φθάνουν στον αμφιβληστροειδή χιτώνα του ματιού δημιουργώντας ηλεκτρικά σήματα που διοχετεύονται δια των οπτικών νεύρων στον εγκέφαλο,όπου και δημιουργείται η αίσθηση της όρασης.</span></span><br />
<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><span style="color: red; text-align: -webkit-auto;"><b>ΦΩΤΟΝΙΑ</b></span></span><br />
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<span style="font-family: "verdana" , sans-serif;"> Στη διάδοση της θερμότητας με ακτινοβολία,η φωτεινή ενέργεια μεταφέρεται με τα φωτόνια.Κάθε φωτόνιο μεταφέρει μια καθορισμένη ποσότητα ενέργειας.<span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;">Φωτόνια που αντιστοιχούν σε φως πράσινου χρώματος έχουν όλα ακριβώς την ίδια ενέργεια.</span>Το ίδιο ακριβώς συμβαίνει και με όλα τα φωτόνια που αντιστοιχούν σε κάποιο συγκεκριμένο χρώμα.Τα φωτόνια όμως που αντιστοιχούν σε διαφορετικά χρώματα μεταξύ τους δεν έχουν την ίδια ενέργεια.Για παράδειγμα,τα φωτόνια του κόκκινου χρώματος έχουν μικρότερη ενέργεια από τα φωτόνια του πράσινου.</span></div>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWJUO_FNB41hI26Skxv_zSyZqfVoL0EFKAJEn07EVuHdVuYg48nEUT939po4FLtxzERG4xFJPu-Fw6Bayfw5EbK-ds73ZQDRhn8osMsVEEdJ6xMuMLyCAO-aX7Wnuo93xLh8RTQTQ4qOkJ/s1600/%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597+%25CE%2593+%25CE%2593%25CE%25A5%25CE%259C%25CE%259D%25CE%2591%25CE%25A3%25CE%2599%25CE%259F%25CE%25A5%2528124%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "verdana" , sans-serif;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWJUO_FNB41hI26Skxv_zSyZqfVoL0EFKAJEn07EVuHdVuYg48nEUT939po4FLtxzERG4xFJPu-Fw6Bayfw5EbK-ds73ZQDRhn8osMsVEEdJ6xMuMLyCAO-aX7Wnuo93xLh8RTQTQ4qOkJ/s400/%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597+%25CE%2593+%25CE%2593%25CE%25A5%25CE%259C%25CE%259D%25CE%2591%25CE%25A3%25CE%2599%25CE%259F%25CE%25A5%2528124%2529.jpg" width="400" /></span></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple; font-family: "verdana" , sans-serif;"><span class="Apple-style-span" style="font-size: small; line-height: 16px; text-align: justify;">Tα φωτόνια απεικονίζονται </span><span style="font-size: small; line-height: 16px; text-align: justify;">συχνά ως τεθλασμένες γραμμές</span> </span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Η φωτεινή ενέργεια μπορεί να μετασχηματιστεί σε άλλες μορφές ενέργειας.Λόγω της διπλής φύσης τους (σωματίδια και κύματα),τα φωτόνια απεικονίζονται </span><span style="font-family: "verdana" , sans-serif;">συχνά ως τεθλασμένες γραμμές.</span><br />
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<b style="line-height: 16px;"><span style="color: red; font-family: "verdana" , sans-serif;">Μ<span style="background-color: white; line-height: 18.2px; text-align: left;">ΕΤ</span><span style="background-color: white; line-height: 18.2px; text-align: left;">Α</span>Σ<span style="background-color: white; line-height: 18.2px; text-align: left;">ΧΗΜ</span><span style="background-color: white; line-height: 18.2px; text-align: left;">Α</span><span style="background-color: white; line-height: 18.2px; text-align: left;">ΤΙ</span>Σ<span style="background-color: white; line-height: 18.2px; text-align: left;">ΜΟΙ ΤΗ</span>Σ<span style="background-color: white; line-height: 18.2px; text-align: left;"> </span><span style="background-color: white; line-height: 18.2px; text-align: left;">Φ</span><span style="background-color: white; line-height: 18.2px; text-align: left;">ΩΤ</span><span style="background-color: white; line-height: 18.2px; text-align: left;">Ε</span><span style="background-color: white; line-height: 18.2px; text-align: left;">ΙΝΗ</span>Σ<span style="background-color: white; line-height: 18.2px; text-align: left;"> </span><span style="background-color: white; line-height: 18.2px; text-align: left;">Ε</span><span style="background-color: white; line-height: 18.2px; text-align: left;">Ν</span><span style="background-color: white; line-height: 18.2px; text-align: left;">Ε</span><span style="background-color: white; text-align: left; white-space: nowrap;">Ρ</span><span style="background-color: white; line-height: 18.2px; text-align: left;">ΓΕΙ</span><span style="background-color: white; line-height: 18.2px; text-align: left;">Α</span>Σ</span></b><br />
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<b style="font-family: Verdana, sans-serif; line-height: 16px;"><span style="color: red;">α) </span><span style="color: blue;">Το φως μετατρέπεται σε θέρμανση</span><span style="color: blue;">.</span></b><br />
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<span style="font-family: "verdana" , sans-serif;"><b> </b>Όταν απορροφώνται τα φωτόνια από τους δομικούς λίθους ενός σώματος,για παράδειγμα τα άτομα ή τα μόρια ενός σώματος,τότε αυξάνεται η κινητική τους ενέργεια με αποτέλεσμα να αυξάνεται η θερμοκρασία του σώματος. </span></div>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm1Sm3LiZQ7wBfdQ5MXjs_0UxGvnHDWHU_LAB2vHLzjXMX1nieJdp4JsrJAmRJ5b6-f9BkpUkJ4X-CWR31OrR3EyB2icaKXlvA-OfYKl0WLLEY0ptwVzSoh2vNUbAFBoRIdqr5Yk_493Fe/s1600/%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597+%25CE%2593+%25CE%2593%25CE%25A5%25CE%259C%25CE%259D%25CE%2591%25CE%25A3%25CE%2599%25CE%259F%25CE%25A5%2528125%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "verdana" , sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm1Sm3LiZQ7wBfdQ5MXjs_0UxGvnHDWHU_LAB2vHLzjXMX1nieJdp4JsrJAmRJ5b6-f9BkpUkJ4X-CWR31OrR3EyB2icaKXlvA-OfYKl0WLLEY0ptwVzSoh2vNUbAFBoRIdqr5Yk_493Fe/s1600/%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597+%25CE%2593+%25CE%2593%25CE%25A5%25CE%259C%25CE%259D%25CE%2591%25CE%25A3%25CE%2599%25CE%259F%25CE%25A5%2528125%2529.jpg" /></span></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Στους ηλιακούς θερμοσίφωνες αξιοποιούμε την ενέργεια του ηλιακού φωτός για να θερμάνουμε το νερό</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Σε αυτή την περίπτωση η φωτεινή ενέργεια μετασχηματίζεται σε θερμική.Για παράδειγμα στους ηλιακούς θερμοσίφωνες αξιοποιούμε την ενέργεια του ηλιακού φωτός για να θερμάνουμε το νερό.</span><br />
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">β)</span><span style="color: blue;"> Το φως </span></b><b><span style="color: blue;">μετατρέπεται σε</span></b><b><span style="color: blue;"> κίνηση</span></b></span><b style="font-family: Verdana, sans-serif; line-height: 16px;">.</b></div>
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<span style="font-family: "verdana" , sans-serif;"> <b><span style="color: blue;">Α</span><span style="color: blue;">κτινόμετρο</span> είναι ένα </b><span style="text-align: -webkit-auto;"><b>όργανο που χρησιμοποιείται για τη μέτρηση της έντασης της θερμότητας της ακτινοβολίας.</b>Χ</span><span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;">ρησιμοποιείται</span><span style="text-align: -webkit-auto;"> στη μετεωρολογία για τη μέτρηση της ηλιακής ακτινοβολίας.</span></span><br />
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<tr><td><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLsO3hp5prykQr5i4quIbEgjUGLMw4vrSNWz_bosYA8sxfQhqZG-CgFfKbHFqtCO8NemwsSEeWtn7vHK1vtau92kJ4l9smJr6zdVtSbAT262FF4aHQT1FpCiF0Vm0xMhATyniiDdsEQg6c/s400/%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597+%25CE%2593+%25CE%2593%25CE%25A5%25CE%259C%25CE%259D%25CE%2591%25CE%25A3%25CE%2599%25CE%259F%25CE%25A5%2528126%2529.jpg" style="margin-left: auto; margin-right: auto;" width="184" /></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><b>Το ακτινόμετρο χρησιμοποιείται στη μετεωρολογία για τη μέτρηση της ηλιακής ακτινοβολίας</b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Όταν εκθέσουμε ένα ακτινόμετρο στο ηλιακό φως ή στο φως ενός επιτραπέζιου φωτιστικού,τότε τα πτερύγιά του περιστρέφονται.Η ενέργεια των φωτονίων που προσπ</span><span style="font-family: "verdana" , sans-serif;">ίπ</span><span style="font-family: "verdana" , sans-serif;">τουν στο ακτινόμετρο μετατρέπεται σε κινητική ενέργεια των πτερυγίων του.</span><br />
<b style="font-family: verdana, sans-serif;"><span style="color: red;"><br /></span></b><b style="font-family: verdana, sans-serif;"><span style="color: red;">γ)</span><span style="color: blue;"> Το φως </span></b><b style="font-family: verdana, sans-serif;"><span style="color: blue;">μετατρέπεται σε</span></b><b style="font-family: verdana, sans-serif;"><span style="color: blue;"> χημικές αντιδράσεις</span></b><b style="font-family: Verdana, sans-serif; line-height: 16px;">.</b><br />
<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><span style="color: blue;"><b> </b></span>Τα πράσινα μέρη των φυτών απορροφούν ορισμένα από τα φωτόνια που προέρχονται από τον ήλιο.Η ενέργεια αυτών των φωτονίων προκαλεί τη χημική αντίδραση που ονομάζεται φωτοσύνθεση.Κατ</span><span style="background-color: white; font-family: "verdana" , sans-serif; line-height: 18.2px; text-align: left;">ά</span><span style="background-color: white; font-family: "verdana" , sans-serif; line-height: 18.2px; text-align: left;"> </span><span style="font-family: "verdana" , sans-serif;"> τη φωτοσύνθεση παράγεται μία χημική ένωση που ονομάζεται γλυκόζη. </span></div>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWnY2MRXn2HDKhyphenhyphenLMC5mlVElJ2C3egz90CQmru4gR9o4Znc9byAom8I_QT_AHrrrrMtXFfhkeR6pbmxdZhjYUrwG98L17xOx8yLvmzPkJYUozSxBSLXTP-21sYIthZOSfdr2rWLT2I9yxo/s1600/%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597+%25CE%2593+%25CE%2593%25CE%25A5%25CE%259C%25CE%259D%25CE%2591%25CE%25A3%25CE%2599%25CE%259F%25CE%25A5%2528127%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "verdana" , sans-serif;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWnY2MRXn2HDKhyphenhyphenLMC5mlVElJ2C3egz90CQmru4gR9o4Znc9byAom8I_QT_AHrrrrMtXFfhkeR6pbmxdZhjYUrwG98L17xOx8yLvmzPkJYUozSxBSLXTP-21sYIthZOSfdr2rWLT2I9yxo/s400/%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597+%25CE%2593+%25CE%2593%25CE%25A5%25CE%259C%25CE%259D%25CE%2591%25CE%25A3%25CE%2599%25CE%259F%25CE%25A5%2528127%2529.jpg" width="400" /></span></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Τα πράσινα μέρη των φυτών απορροφούν ορισμένα από τα φωτόνια που προέρχονται από τον ήλιο</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Με τη φωτοσύνθεση η φωτεινή ενέργεια μετατρέπεται σε χημική που αποθηκεύεται στη γλυκόζη,που είναι οι θρεπτικές ουσίες των φυτών</span><span style="text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;">.Κατά την φωτοσύνθεση στα φυτά η φωτεινή ενέργεια δεσμεύεται και χρησιμοποιείται για τη μετατροπή διοξειδίου του άνθρακα και νερού σε οξυγόνο και ενεργειακά πλούσιες οργανικές ενώσεις,κυρίως υδατάνθρακες.</span></span><br />
<b style="font-family: verdana, sans-serif;"><span style="color: red;"><br /></span></b><b style="font-family: verdana, sans-serif;"><span style="color: red;">δ)</span><span style="color: blue;"> Το φως </span></b><b style="font-family: verdana, sans-serif;"><span style="color: blue;">μετατρέπεται σε</span></b><b style="font-family: verdana, sans-serif;"><span style="color: blue;"> ηλεκτρικό ρεύμα</span></b><b style="font-family: Verdana, sans-serif; line-height: 16px;">.</b></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><span style="color: blue;"><b> </b></span>Τα φωτοβολταϊκά στοιχεία είναι συσκευές που μετασχηματίζουν τη φωτεινή ενέργεια σε ηλεκτρική. </span></div>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4vd9HK_nkjr_pdnmLjnjZWfmO1V9dsaIIHaMCSXj2LMWuJiGIszKh3dcGGIhpd5DKcKuD8KGsYV6lSb5pzDQPShQj45kOVUDigjKxrsaxQzRNMHerQjQStrTw9dojUIw0jB2AEY-Y3E58/s1600/%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597+%25CE%2593+%25CE%2593%25CE%25A5%25CE%259C%25CE%259D%25CE%2591%25CE%25A3%25CE%2599%25CE%259F%25CE%25A5%2528128%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "verdana" , sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4vd9HK_nkjr_pdnmLjnjZWfmO1V9dsaIIHaMCSXj2LMWuJiGIszKh3dcGGIhpd5DKcKuD8KGsYV6lSb5pzDQPShQj45kOVUDigjKxrsaxQzRNMHerQjQStrTw9dojUIw0jB2AEY-Y3E58/s1600/%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597+%25CE%2593+%25CE%2593%25CE%25A5%25CE%259C%25CE%259D%25CE%2591%25CE%25A3%25CE%2599%25CE%259F%25CE%25A5%2528128%2529.jpg" /></span></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Στα ηλιακά αυτοκίνητα αλλά υπάρχουν φωτοβολταϊκά στοιχεία στα οποία η φωτεινή ενέργεια μετατρέπεται σε ηλεκτρική</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Στους υπολογιστές τσέπης,στα ηλιακά αυτοκίνητα αλλά και σε διαστημικά οχήματα υπάρχουν φωτοβολταϊκά στοιχεία στα οποία η φωτεινή ενέργεια μετατρέπεται σε ηλεκτρική.</span><br />
<b style="font-family: verdana, sans-serif;"><span style="color: red;"><br /></span></b><b style="font-family: verdana, sans-serif;"><span style="color: red;">ε) </span><span style="color: blue;">Το φως </span></b><b style="font-family: verdana, sans-serif;"><span style="color: blue;">μετατρέπεται σε</span></b><b style="font-family: verdana, sans-serif;"><span style="color: blue;"> όραση</span></b><b style="font-family: Verdana, sans-serif; line-height: 16px;">.</b></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"> Όταν φθάσει στα μάτια μας φως προκαλούνται χημικές αντιδράσεις στα οπτικά κύτταρα </span><span style="font-family: "verdana" , sans-serif;">και τελικά η φωτεινή ενέργεια μετατρέπεται σε χημική και στη συνέχεια σε ηλεκτρική.</span></div>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAY2Mvub35FYcQuMorhcNcWvlJK_CEK0eU9TJdnB_ttZdOkenEVsyNj56Pa0kKTNIMbWTzm3ehrjfhU-y_H7uAC-y2Jp-ajsApqkSrdB_FCE8QkwYHyIB4BrIhjVxLhZ8CsiBQWDO8Y5UX/s1600/%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597+%25CE%2593+%25CE%2593%25CE%25A5%25CE%259C%25CE%259D%25CE%2591%25CE%25A3%25CE%2599%25CE%259F%25CE%25A5%2528129%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "verdana" , sans-serif;"><img border="0" height="285" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAY2Mvub35FYcQuMorhcNcWvlJK_CEK0eU9TJdnB_ttZdOkenEVsyNj56Pa0kKTNIMbWTzm3ehrjfhU-y_H7uAC-y2Jp-ajsApqkSrdB_FCE8QkwYHyIB4BrIhjVxLhZ8CsiBQWDO8Y5UX/s400/%25CE%25A6%25CE%25A5%25CE%25A3%25CE%2599%25CE%259A%25CE%2597+%25CE%2593+%25CE%2593%25CE%25A5%25CE%259C%25CE%259D%25CE%2591%25CE%25A3%25CE%2599%25CE%259F%25CE%25A5%2528129%2529.jpg" width="400" /></span></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">Όταν φθάσει στα μάτια μας φως προκαλούνται χημικές αντιδράσεις στα οπτικά κύτταρα </span><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">και τελικά η φωτεινή ενέργεια μετατρέπεται σε χημική και στη συνέχεια σε ηλεκτρική</span></span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Το ηλεκτρικό σήμα που παράγεται μεταφέρεται μέσω του οπτικού νεύρου στον εγκέφαλο και έτσι δημιουργείται το αίσθημα της όρασης.</span></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-82240854039838023242016-11-14T17:54:00.000-08:002020-09-12T09:54:52.665-07:00ΠΕΔΙΟ ΧΑΜΗΛΟΥ ΒΑΡΟΜΕΤΡΙΚΟΥ<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="color: red; font-family: verdana, sans-serif; text-align: justify;"><span style="font-size: x-large;">ΠΕΔΙΟ ΧΑΜΗΛΟΥ ΒΑΡΟΜΕΤΡΙΚΟΥ</span></b><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="color: purple; font-family: Verdana, sans-serif; font-size: large;"><b>ΠΕΔΙΟ ΧΑΜΗΛΟΥ ΒΑΡΟΜΕΤΡΙΚΟΥ</b></span></td></tr>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΕΙΣΑΓΩΓΗ</b></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><br /></span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b><span style="color: blue;">Κυκλώνας </span>ονομάζεται η περιοχή με χαμηλή βαρομετρική πίεση.Η ονομασία κυκλώνας χρησιμοποιείται μόνο για τις τροπικές περιοχές,ενώ σε όλα τα άλλα μέρη λέγεται ύφεση και σημαίνει την περιοχή όπου ο αέρας είναι θερμός και αραιός</b>.</span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="font-size: small;"><b style="font-family: Verdana, sans-serif; text-align: justify;"><span style="color: purple;">Κυκλώνας ονομάζεται η περιοχή με χαμηλή βαρομετρική πίεση.Η ονομασία κυκλώνας χρησιμοποιείται μόνο για τις τροπικές περιοχές,ενώ σε όλα τα άλλα μέρη λέγεται ύφεση και σημαίνει την περιοχή όπου ο αέρας είναι θερμός και αραιός</span></b><span style="font-family: "verdana" , sans-serif; line-height: 1.5em; text-align: justify;"> </span></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Οι άνεμοι στους κυκλώνες και στις υφέσεις κινούνται από την περίμετρο προς την κεντρική ζώνη,με κατεύθυνση στο βόρειο ημισφαίριο,αντίθετη με την κίνηση των δεικτών του ρολογιού.Το αντίθετο συμβαίνει στο νότιο ημισφαίριο.</span><br />
<span style="font-family: Verdana, sans-serif;"><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> </span><span style="background-color: white; color: #252525; text-align: start;">Πρόκειται για περιοχή όπου επικρατούν χαμηλότερες τιμές </span>ατμοσφαιρικής πίεσης<span style="background-color: white; color: #252525; text-align: start;"> από τις γειτονικές περιοχές.Λόγω του ορισμού του,ένα χαμηλό βαρομετρικό σε μία περιοχή της γης μπορεί να έχει κέντρο <b>1015 hPa</b>,ενώ ένα </span>υψηλό βαρομετρικό<span style="background-color: white; color: #252525; text-align: start;"> σε κάποια μακρινή περιοχή μπορεί να έχει πίεση <b>1010 hPa </b>στο κέντρο του.</span></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><br /></span><span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΧΑΡΑΚΤΗΡΙΣΤΙΚΑ ΤΟΥ ΚΥΚΛΩΝΑ</b></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><br /></span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b>Οι άνεμοι στις περιοχές των κυκλώνων φτάνουν την ταχύτητα των 130 μιλίων την ώρα,ενώ στις περιοχές των υφέσεων δεν ξεπερνούν την ταχύτητα των 80 μιλίων την ώρα.</b>Οι κυκλώνες σχηματίζονται στις τροπικές περιοχές και σε πλάτος<b> 5°</b> ως <b>20°</b> από τις δύο πλευρές του ισημερινού.Κινούνται με ταχύτητα <b>15</b> ως <b>20 μιλίων</b> την ώρα και βασικό πεδίο δράσης τους είναι οι ωκεανοί.Πολλές φορές όμως εμφανίζονται στα παράλια των ηπείρων και στα νησιά και προκαλούν τρομερές καταστροφές.Οι κυκλώνες των περιοχών του ισημερινού λέγονται τυφώνες και ο καθένας χαρακτηρίζεται από ένα όνομα,συνήθως γυναικείο (π.χ. <b>Βέρα, Μαίρη</b> κ.ά.).</span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4oA09BAEs9N7hsQHaNj2i4TTnBK7qtTIVyPPixF3wKkFv65rufKS0QziocSLsfRo4UAlnfj_k245u7qdze3tt4OkwXhPna9SsPFXwrJ-onhqH_wk0eAvl96lCUUSqPo1rUW0_KYxwE_A/s1600/%25CE%259A%25CE%259B%25CE%2599%25CE%259C%25CE%2591%25CE%25A4%25CE%259F%25CE%259B%25CE%259F%25CE%2593%25CE%2599%25CE%2591%25285%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4oA09BAEs9N7hsQHaNj2i4TTnBK7qtTIVyPPixF3wKkFv65rufKS0QziocSLsfRo4UAlnfj_k245u7qdze3tt4OkwXhPna9SsPFXwrJ-onhqH_wk0eAvl96lCUUSqPo1rUW0_KYxwE_A/s400/%CE%9A%CE%9B%CE%99%CE%9C%CE%91%CE%A4%CE%9F%CE%9B%CE%9F%CE%93%CE%99%CE%91(5).jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="font-family: "verdana" , sans-serif; text-align: justify;"><b><span style="color: purple; font-size: small;">Οι άνεμοι στις περιοχές των κυκλώνων φτάνουν την ταχύτητα των 130 μιλίων την ώρα</span></b></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b>Σε έναν κυκλώνα οι άνεμοι περιστρέφονται γύρω από μια στήλη κενού και μπορούν να σηκώσουν ένα ολόκληρο κτίριο ή να ξεριζώσουν πελώρια δέντρα.</b>Στη σύγχρονη εποχή η ανάπτυξη της μετεωρολογίας,οι μετεωρολογικοί δορυφόροι και οι ειδικές ιπτάμενες υπηρεσίες επισημαίνουν τους κυκλώνες και προσδιορίζουν με ακρίβεια την κατεύθυνσή τους,ώστε να είναι δυνατή η λήψη των απαραίτητων μέτρων για τη μείωση των καταστροφών στο ελάχιστο.Η πορεία των κυκλώνων σημειώνεται πάνω σε ειδικούς μετεωρολογικούς χάρτες,ώστε να είναι δυνατός ο εντοπισμός των περιοχών που δοκιμάζονται περισσότερο και συχνότερα.</span></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-87161201854963850402016-11-14T17:37:00.000-08:002020-09-12T09:54:52.860-07:00ΠΕΔΙΟ ΥΨΗΛΟΥ ΒΑΡΟΜΕΤΡΙΚΟΥ<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="color: red; font-family: Verdana, sans-serif; line-height: 1.5em; text-align: justify;"><span style="font-size: x-large;">ΠΕΔΙΟ ΥΨΗΛΟΥ ΒΑΡΟΜΕΤΡΙΚΟΥ</span></b><br />
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<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-family: Verdana, sans-serif; font-size: large;">ΠΕΔΙΟ ΥΨΗΛΟΥ ΒΑΡΟΜΕΤΡΙΚΟΥ</span></b></td></tr>
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<div style="line-height: 1.5em; text-align: justify;">
<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΕΙΣΑΓΩΓΗ</b></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><br /></span>
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Η καιρική κατάσταση ενός τόπου επηρεάζεται από τη δημιουργία αντικυκλώνων και κυκλώνων,με αποτέλεσμα στο χρονικό διάστημα της επίδρασης να δημιουργούνται ακρότητες στους τοπικούς καιρικούς παράγοντες.</span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9BA32OQCGPj04DyhKq6_fW_bu-_JaejQzU3lYUSrhfQjYx41Qeda57dDIc97O0ERBgSURHJ3kwOHWNSJ39qXrHsuoRDU02GOReqYILW3HTLWmPf6I7yzAnEkHAchTtoBLwIXr-D8bVm8/s1600/%25CE%2591%25CE%259D%25CE%25A4%25CE%2599%25CE%259A%25CE%25A5%25CE%259A%25CE%259B%25CE%25A9%25CE%259D%25CE%2591%25CE%25A3.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9BA32OQCGPj04DyhKq6_fW_bu-_JaejQzU3lYUSrhfQjYx41Qeda57dDIc97O0ERBgSURHJ3kwOHWNSJ39qXrHsuoRDU02GOReqYILW3HTLWmPf6I7yzAnEkHAchTtoBLwIXr-D8bVm8/s1600/%25CE%2591%25CE%259D%25CE%25A4%25CE%2599%25CE%259A%25CE%25A5%25CE%259A%25CE%259B%25CE%25A9%25CE%259D%25CE%2591%25CE%25A3.gif" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="text-align: justify;"><span style="color: purple; font-family: Verdana, sans-serif; font-size: small;">Αντικυκλώνας ονομάζεται η περιοχή υψηλής βαρομετρικής πίεσης,όπου οι ισοβαρείς καμπύλες που την περιβάλλουν προχωρούν από το κέντρο προς τις περιφέρειες με πίεση που συνεχώς ελαττώνεται</span></b></td></tr>
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<span style="font-family: verdana, sans-serif;"><span style="color: blue;"> </span><span style="color: blue; font-weight: bold;">Αντικυκλώνας </span><b>ονομάζεται η περιοχή υψηλής βαρομετρικής πίεσης,όπου οι ισοβαρείς καμπύλες που την περιβάλλουν προχωρούν από το κέντρο προς τις περιφέρειες με πίεση που συνεχώς ελαττώνεται.</b></span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIYyEbP8Ufh3zmPZe0VbgaOlqyGUJNdqS3F8z9JvNPmUQ858STmx_pPvljz6ERpWCjrS3A5XFguktrYaBPKz51pptTXGzlJAIl1bm6FTiHsEmaL29lBiSfIzDfSlnEJUlBoDOg7WrkO9s/s1600/%25CE%259A%25CE%259B%25CE%2599%25CE%259C%25CE%2591%25CE%25A4%25CE%259F%25CE%259B%25CE%259F%25CE%2593%25CE%2599%25CE%2591%25283%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIYyEbP8Ufh3zmPZe0VbgaOlqyGUJNdqS3F8z9JvNPmUQ858STmx_pPvljz6ERpWCjrS3A5XFguktrYaBPKz51pptTXGzlJAIl1bm6FTiHsEmaL29lBiSfIzDfSlnEJUlBoDOg7WrkO9s/s400/%25CE%259A%25CE%259B%25CE%2599%25CE%259C%25CE%2591%25CE%25A4%25CE%259F%25CE%259B%25CE%259F%25CE%2593%25CE%2599%25CE%2591%25283%2529.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple; font-family: Verdana, sans-serif; font-size: small;">Χαρακτηριστικό γνώρισμα των αντικυκλώνων είναι το ότι κατά τη διάρκεια της παρουσίας τους η πίεση σε έναν τόπο είναι μεγαλύτερη από την κανονική</span></b></td></tr>
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<span style="background-color: white; text-align: start;"><span style="font-family: verdana, sans-serif;"><b> </b></span></span><span style="background-color: white; font-family: Verdana, sans-serif; text-align: start;">Χαρακτηριστικό γνώρισμα των αντικυκλώνων είναι το ότι κατά τη διάρκεια της παρουσίας τους η πίεση σε έναν τόπο είναι μεγαλύτερη από την κανονική.Επίσης οι άνεμοι έχουν κυκλική τροχιά και είναι ισχυρότεροι στην περιφέρεια του νοητού κύκλου απ' ότι στο κέντρο του.</span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6rSzmeVDhxi6-rer2mWVqM3oE5BjmLSuS89YU4oei3K9l9JHHfKcKXpP1zd-vtObpBFLTz1URXpMyrNBVLj2puIdq0a_DNE5qF4Q4meQp3iB7LGlIisciK5JQTw8TfVUkTCZO_oJDxS8/s1600/%25CE%259F+%25CE%25B1%25CE%25BD%25CF%2584%25CE%25B9%25CE%25BA%25CF%2585%25CE%25BA%25CE%25BB%25CF%258E%25CE%25BD%25CE%25B1%25CF%2582+%25CE%25B5%25CE%25AF%25CE%25BD%25CE%25B1%25CE%25B9+%25CF%2584%25CE%25BF+%25CE%25B1%25CE%25BD%25CF%2584%25CE%25AF%25CE%25B8%25CE%25B5%25CF%2584%25CE%25BF+%25CF%2586%25CE%25B1%25CE%25B9%25CE%25BD%25CF%258C%25CE%25BC%25CE%25B5%25CE%25BD%25CE%25BF+%25CF%2584%25CE%25BF%25CF%2585+%25CE%25BA%25CF%2585%25CE%25BA%25CE%25BB%25CF%258E%25CE%25BD%25CE%25B1+%25CE%25BA%25CE%25B1%25CF%2584%25CE%25AC+%25CF%2584%25CE%25BF%25CE%25BD+%25CE%25BF%25CF%2580%25CE%25BF%25CE%25AF%25CE%25BF+%25CE%25B7+%25CF%2580%25CE%25AF%25CE%25B5%25CF%2583%25CE%25B7+%25CE%25B5%25CE%25AF%25CE%25BD%25CE%25B1%25CE%25B9+%25CF%2587%25CE%25B1%25CE%25BC%25CE%25B7%25CE%25BB%25CE%25AE..jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="208" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6rSzmeVDhxi6-rer2mWVqM3oE5BjmLSuS89YU4oei3K9l9JHHfKcKXpP1zd-vtObpBFLTz1URXpMyrNBVLj2puIdq0a_DNE5qF4Q4meQp3iB7LGlIisciK5JQTw8TfVUkTCZO_oJDxS8/s400/%25CE%259F+%25CE%25B1%25CE%25BD%25CF%2584%25CE%25B9%25CE%25BA%25CF%2585%25CE%25BA%25CE%25BB%25CF%258E%25CE%25BD%25CE%25B1%25CF%2582+%25CE%25B5%25CE%25AF%25CE%25BD%25CE%25B1%25CE%25B9+%25CF%2584%25CE%25BF+%25CE%25B1%25CE%25BD%25CF%2584%25CE%25AF%25CE%25B8%25CE%25B5%25CF%2584%25CE%25BF+%25CF%2586%25CE%25B1%25CE%25B9%25CE%25BD%25CF%258C%25CE%25BC%25CE%25B5%25CE%25BD%25CE%25BF+%25CF%2584%25CE%25BF%25CF%2585+%25CE%25BA%25CF%2585%25CE%25BA%25CE%25BB%25CF%258E%25CE%25BD%25CE%25B1+%25CE%25BA%25CE%25B1%25CF%2584%25CE%25AC+%25CF%2584%25CE%25BF%25CE%25BD+%25CE%25BF%25CF%2580%25CE%25BF%25CE%25AF%25CE%25BF+%25CE%25B7+%25CF%2580%25CE%25AF%25CE%25B5%25CF%2583%25CE%25B7+%25CE%25B5%25CE%25AF%25CE%25BD%25CE%25B1%25CE%25B9+%25CF%2587%25CE%25B1%25CE%25BC%25CE%25B7%25CE%25BB%25CE%25AE..jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="color: purple; font-family: Verdana, sans-serif; font-size: small;"><b>Ένα υψηλό βαρομετρικό σε μία περιοχή της γης μπορεί να έχει κέντρο 1010 hPa,ενώ ένα <span style="text-align: justify;">χαμηλό βαρομετρικό</span><span style="background-color: white; text-align: start;"> σε κάποια μακρινή περιοχή μπορεί να έχει πίεση 1015 hPa στο κέντρο του</span></b></span></td></tr>
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<span style="background-color: white; font-family: Verdana, sans-serif; text-align: start;"> Πρόκειται για περιοχή όπου επικρατούν υψηλότερες τιμές </span><span style="font-family: Verdana, sans-serif;">ατμοσφαιρικής πίεσης</span><span style="background-color: white; font-family: Verdana, sans-serif; text-align: start;"> από τις γειτονικές περιοχές.Λόγω του ορισμού του,ένα υψηλό βαρομετρικό σε μία περιοχή της γης μπορεί να έχει κέντρο <b>1010 hPa</b>,ενώ ένα </span><span style="font-family: Verdana, sans-serif;">χαμηλό βαρομετρικό</span><span style="background-color: white; font-family: Verdana, sans-serif; text-align: start;"> σε κάποια μακρινή περιοχή μπορεί να έχει πίεση<b> 1015 hPa</b> στο κέντρο του.</span><br />
<span style="background-color: white; font-family: Verdana, sans-serif; text-align: start;"> Ο<b> αντικυκλώνας </b>είναι το αντίθετο φαινόμενο του <b>κυκλώνα</b> κατά τον οποίο η πίεση είναι χαμηλή.</span><br />
<span class="Apple-style-span" style="font-family: Verdana, sans-serif;"><span style="background-color: white; font-family: sans-serif; font-size: 12.7px; text-align: start;"><br /></span></span>
<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΧΑΡΑΚΤΗΡΙΣΤΙΚΑ ΤΟΥ ΑΝΤΙΚΥΚΛΩΝΑ</b></span><br />
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<b style="font-family: verdana, sans-serif;"> Η υψηλή πίεση της περιοχής του αντικυκλώνα σημαίνει ότι ο ατμοσφαιρικός αέρας είναι πυκνός και επομένως ψυχρός.Οι άνεμοι στις περιοχές των αντικυκλώνων κινούνται από το κέντρο προς την περιμετρική ζώνη,με την κατεύθυνση των δεικτών του ρολογιού στο βόρειο ημισφαίριο και με αντίθετη κατεύθυνση στο νότιο.</b><span style="font-family: "verdana" , sans-serif;"> </span><br />
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<tr><td class="tr-caption" style="font-size: 13px;"><span style="font-family: "verdana" , sans-serif; font-size: small; text-align: justify;"><b><span style="color: purple;">Οι άνεμοι στις περιοχές των αντικυκλώνων κινούνται από το κέντρο προς την περιμετρική ζώνη,με την κατεύθυνση των δεικτών του ρολογιού στο βόρειο ημισφαίριο και με αντίθετη κατεύθυνση στο νότιο</span></b></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Η κίνηση αυτή έχει ως συνέπεια ψυχρές αέριες μάζες να κινούνται στις περιμετρικές ζώνες και να δημιουργούν νέφωση,που συχνά συνοδεύεται από χιονοπτώσεις.Αντίθετα,στο κέντρο του αντικυκλώνα η ατμόσφαιρα είναι σχεδόν στατική,ο ήλιος λαμπρός,η θερμοκρασία όμως είναι χαμηλή.</span><br />
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΤΥΠΟΙ ΑΝΤΙΚΥΚΛΩΝΑ</b></span><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b>Διακρίνουμε δύο τύπους αντικυκλώνων,τους μόνιμους και τους κινητούς.</b>Οι μόνιμοι επικρατούν σε δύο κυρίως ζώνες, μια στο βόρειο και μια στο νότιο ημισφαίριο και σε πλάτος από <b>20° </b>ως <b>30°</b>.Ένας κινητός αντικυκλώνας επιδρά σε μια περιοχή πρώτα με την εξωτερική του ζώνη και δημιουργεί ανέμους,πτώση της θερμοκρασίας,νέφωση και χιονόπτωση,μετά με την κεντρική του ζώνη της ηρεμίας,και τελικά στην έξοδό του δημιουργεί τα αντίστοιχα με την είσοδό του φαινόμενα.Ο καιρός στην <b>Ελλάδα </b>επηρεάζεται βασικά από τους αντικυκλώνες της <b>Σιβηρίας </b>και των <b>Αζορών νησιών.</b></span></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-87105803189517533272016-11-10T18:41:00.002-08:002020-09-12T09:54:53.056-07:00ΑΤΜΟΣΦΑΙΡΙΚΗ ΠΙΕΣΗ<div dir="ltr" style="text-align: left;" trbidi="on">
<strong style="background-color: white; font-family: 'Trebuchet MS', Trebuchet, sans-serif; line-height: 16px; text-align: -webkit-auto;"><span class="Apple-style-span" style="color: red;"><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; font-size: x-large;">ΑΤΜΟΣΦΑΙΡΙΚΗ ΠΙΕΣΗ</span></span></strong><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: large;"><b>ΑΤΜΟΣΦΑΙΡΙΚΗ ΠΙΕΣΗ</b></span></td></tr>
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<span style="color: red; font-family: "verdana" , sans-serif;"><b>ΕΙΣΑΓΩΓΗ</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"> Είναι γνωστό ότι η γη περιβάλλεται από ένα στρώμα αέρα που λέγεται ατμόσφαιρα.</span><span style="font-family: "verdana" , sans-serif;"><b>Η ατμόσφαιρα αποτελείται από ένα μείγμα αερίων που ονομάζεται <span style="color: blue;">ατμοσφαιρικός αέρας</span>.</b></span></div>
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<tr><td class="tr-caption" style="font-size: 13px;"><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; text-align: justify;"><b>Α</b></span><span style="font-family: "verdana" , sans-serif; font-size: small; text-align: justify;"><b>τμόσφαιρα ονομάζεται ένα λεπτό στρώμα αερίων που περιβάλλει περιβάλλει τη Γη</b></span></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"><b> <span style="color: blue;">Α</span></b></span><span style="font-family: "verdana" , sans-serif;"><b><span style="color: blue;">τμόσφαιρα </span>ονομάζεται ένα λεπτό στρώμα αερίων που περιβάλλει περιβάλλει τη Γη.</b></span><span style="font-family: "verdana" , sans-serif;">Εάν η Γη είχε μέγεθος μπάλας μπάσκετ, η ατμόσφαιρα θα είχε πάχος ενός φύλλου χαρτιού.</span></div>
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<span style="font-family: "verdana" , sans-serif;"> Η σ</span><span style="font-family: "verdana" , sans-serif;">ύνθεση της ατμόσφαιρας είναι:</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: blue;">Άζωτο</span><span style="color: red;"> </span><span style="color: red;"> (</span><span style="color: red;">78%</span><span style="color: red;">),</span><span style="color: red;"> </span></b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: blue;">Οξυγόνο</span><span style="color: red;"> </span><span style="color: red;">(</span><span style="color: red;">21%</span><span style="color: red;">), </span></b></span></div>
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<span style="color: red;"><span style="font-family: "verdana" , sans-serif;"><b><span style="color: blue;">Άλλα αέρια</span><span style="color: red;"> </span>(<span style="color: red;">1%</span>) </b></span><span style="font-family: "verdana" , sans-serif;"> </span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"> Ο αέρας είναι διαφανής.Έχει μάζα και από τη γη ασκείται σε αυτόν η δύναμη του βάρους. Επομένως, όπως συμβαίνει με όλα τα ρευστά σώματα,ασκεί πίεση σε κάθε επιφάνεια που βρίσκεται μέσα σ' αυτόν</span><span style="font-family: "verdana" , sans-serif;">.Όπως ακριβώς η υδροστατική πίεση μιας κατακόρυφης στήλης νερού οφείλεται στο βάρος της,έτσι και η ατμοσφαιρική πίεση οφείλεται στο βάρος του αέρα.</span></div>
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<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">Η σ</span><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">ύνθεση της ατμόσφαιρας</span></span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Ο αέρας,όπως και κάθε άλλο σώμα,έλκεται από τη γη,και η έλξη αυτή συγκρατεί τα μόρια του και δεν τα αφήνει να φύγουν προς το διάστημα.Εξαιτίας της γήινης έλξεως ο αέρας έχει βάρος,το οποίο προκαλεί πίεση στην επιφάνεια της γης,αλλά και σε κάθε άλλη επιφάνεια που βρίσκεται σε επαφή με τον αέρα.</span><span style="font-family: "verdana" , sans-serif;">Η πίεση αυτή ονομάζεται </span><strong style="font-family: Verdana, sans-serif;">ατμοσφαιρική πίεση.</strong></div>
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<span style="color: red; font-family: "verdana" , sans-serif;"><span style="line-height: 16px;"><b>ΑΤΜΟΣΦΑΙΡΙΚΗ ΠΙΕΣΗ</b></span></span><br />
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<span style="font-family: "verdana" , sans-serif;"><span style="color: blue;"> </span><span style="color: blue; font-weight: bold;">Ατμοσφαιρική πίεση</span><b> ονομάζεται η πίεση που δημιουργείται από την ατμόσφαιρα.</b></span><br />
<span style="font-family: "verdana" , sans-serif;"> Η τιμή της ατμοσφαιρικής πίεσης εξαρτάται από το ύψος από την επιφάνεια της θάλασσας.<span style="text-align: -webkit-auto;">Όσο μεγαλύτερο είναι το υψόμετρο στο οποίο βρισκόμαστε τόσο μικρότερη είναι η ατμοσφαιρική πίεση γιατί είναι λιγότερη η ποσότητα του αέρα που βρίσκεται πάνω από εμάς και μας πιέζει με το βάρος της.</span></span><br />
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<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><span style="line-height: 16px; text-align: justify;">Η τιμή της ατμοσφαιρικής πίεσης εξαρτάται από το ύψος από την επιφάνεια της θάλασσας.</span><span style="font-family: "verdana" , sans-serif; line-height: 16px;">Όσο μεγαλύτερο είναι το υψόμετρο στο οποίο βρισκόμαστε τόσο μικρότερη είναι η ατμοσφαιρική πίεση</span></span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Τα ανώτερα στρώματα της ατμόσφαιρας πιέζουν,λόγω του βάρους τους,τα κατώτερα με αποτέλεσμα η τιμή της πίεσης να είναι μεγαλύτερη στην επιφάνεια της θάλασσας.</span><span style="font-family: "verdana" , sans-serif;">Αντιλαμβανόμαστε την ατμοσφαιρική πίεση μόνο όταν υπάρχει διαφορά πίεσης.</span><br />
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<tr><td class="tr-caption" style="font-size: 13px;"><span style="color: purple; font-size: small;"><span style="font-family: "verdana" , sans-serif; line-height: 16px; text-align: justify;"><b>Π</b></span><b style="line-height: 16px; text-align: justify;"><span style="font-family: "verdana" , sans-serif;">ίεση μιας ατμόσφαιρας</span><span style="font-family: "verdana" , sans-serif;"> (1 atm) ονομάζεται </span><span style="font-family: "verdana" , sans-serif;">τιμή της ατμοσφαιρικής πίεσης στην επιφάνεια της θάλασσας</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> <b><span style="color: blue;">Π</span></b></span><b><span style="font-family: "verdana" , sans-serif;"><span style="color: blue;">ίεση μιας ατμόσφαιρας</span></span><span style="font-family: "verdana" , sans-serif;"><span style="color: blue;"> (</span><span style="color: red;">1 atm</span><span style="color: blue;">) </span>ονομάζεται </span><span style="font-family: "verdana" , sans-serif;">τιμή της ατμοσφαιρικής πίεσης στην επιφάνεια της θάλασσας</span><span style="font-family: "verdana" , sans-serif;">.</span></b><br />
<b><span style="font-family: "verdana" , sans-serif;"> </span></b><span style="text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;">Η τιμή αυτή σημαίνει ότι σε κάθε τετραγωνικό μέτρο επιφάνειας ασκείται δύναμη <b>100000 Ν!</b>Η επιφάνεια του σώματος μας είναι περίπου ένα με δύο τετραγωνικά μέτρα και άρα και το σώμα μας δέχεται από τον ατμοσφαιρικό αέρα μια τόσο μεγάλη δύναμη η οποία κανονικά έπρεπε να μας συνθλίψει.Το σώμα μας όμως είναι φτιαγμένο ώστε να έχει την ίδια πίεση στο εσωτερικό του και έτσι να αντισταθμίζεται και να εξουδετερώνεται η επίδραση της ατμοσφαιρικής πίεσης που ασκείται εξωτερικά. </span></span></div>
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<strong><span style="color: red; font-family: "verdana" , sans-serif;">ΕΞΗΓΗΣΗ ΤΗΣ ΑΤΜΟΣΦΑΙΡΙΚΗΣ ΠΙΕΣΗΣ</span></strong></div>
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<span style="font-family: "verdana" , sans-serif;"> Ένα απλό πείραμα που αποδεικνύει την ύπαρξη της ατμοσφαιρικής πίεσης είναι αυτό με τον ελαστικό δίσκο,την γνωστή μας βεντούζα.Αν εφαρμόσουμε τον ελαστικό δίσκο σε κάποια λεία επιφάνεια,για παράδειγμα στο τζάμι,και επιχειρήσουμε να τον αποκολλήσουμε τραβώντας τον άγκιστρο,θα συναντήσουμε μεγάλη δυσκολία.Αν όμως ανασηκώσουμε λίγο τα χείλη του,ώστε να περάσει αέρας ανάμεσα στο δίσκο και στο τζάμι,η αποκόλληση γίνεται χωρίς προσπάθεια.</span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDkhO1oHfcNwrh4ZGD74GGnRdKCUCauMTqA3GKiQLdT4XsBmkDaz0HjXpLUM9ijwY_0zyu91a6_3yqcB_IsPlpvRgkZSTSKrgnFiWO5WzrQ15z14qIj0aRJUyVt0HDFoLbB_gpZSBQ2U17/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(160).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="170" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDkhO1oHfcNwrh4ZGD74GGnRdKCUCauMTqA3GKiQLdT4XsBmkDaz0HjXpLUM9ijwY_0zyu91a6_3yqcB_IsPlpvRgkZSTSKrgnFiWO5WzrQ15z14qIj0aRJUyVt0HDFoLbB_gpZSBQ2U17/s200/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(160).JPG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Η βεντούζα με άγκιστρο</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-family: "verdana" , sans-serif; font-size: 13px;"> </span><span style="font-family: "verdana" , sans-serif;">Το φαινόμενο εξηγείται ως εξής:</span></span><br />
<span style="font-family: "verdana" , sans-serif;"><span style="font-family: "verdana" , sans-serif;"> Όταν δεν υπάρχει αέρας ανάμεσα στο δίσκο και το τζάμι,ο δίσκος πιέζεται μόνο από την έξω επιφάνεια του και κολλάει στο τζάμι.Όταν όμως μπαίνει αέρας ανάμε</span><span style="font-family: "verdana" , sans-serif;">σα στο δίσκο και το τζάμι,αναπτύσσεται πιεστική δύναμη και στη μέσα επιφάνεια του δίσκου και ο δίσκος αποχωρίζεται εύκολα.</span></span></div>
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<span style="font-family: "verdana" , sans-serif;"> Ένα άλλο πείραμα που φανερώνει την ύπαρξη της ατμοσφαιρικής πιέσεως είναι και το ακόλουθο.</span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUUkfe_bqvqIGfs0f6ptsF1p3tjo10_6T42loxwJQftmnRLBose2kM2Lzqqy-xiyUjNln_lVoN4YqqKKyjjxf0wyCUIavaJkHIOL947w11MG8ko8OjWNeXzSvDIm_45BS97dlInBMwAX11/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(161).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUUkfe_bqvqIGfs0f6ptsF1p3tjo10_6T42loxwJQftmnRLBose2kM2Lzqqy-xiyUjNln_lVoN4YqqKKyjjxf0wyCUIavaJkHIOL947w11MG8ko8OjWNeXzSvDIm_45BS97dlInBMwAX11/s200/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(161).JPG" width="155" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Προσαρμόζουμε μία ελαστική μεμβράνη στο μεγάλο στόμιο ενός χωνιού και μετά ρουφάμε τον αέρα από το χωνί</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Προσαρμόζουμε μία ελαστική μεμβράνη στο μεγάλο στόμιο ενός χωνιού και μετά ρουφάμε τον αέρα από το χωνί.Το γεγονός αυτό φανερώνει ότι κάποια δύναμη ενεργεί πάνω στην εξωτερική επιφάνεια της μεμβράνης και τη σπρώχνει προς τα μέσα.Φυσικά η δύναμη αυτή δεν εμφανίζεται τη στιγμή που αφαιρούμε τον αέρα από το χωνί,αλλά υπάρχει από πριν,αν και δε γίνεται αντιληπτοί στην αρχή,γιατί η επιφάνεια πιέζεται εξίσου και από τις δύο όψεις<b> (F'=F).</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"> Αφαιρώντας τον αέρα μικραίνει η εσωτερική πίεση,άρα και η πιεστική δύναμη <b>F',</b>καταστρέφεται η ισορροπία και η μεμβράνα ωθείται προς τα μέσα,ώσπου βρίσκει άλλη θέση ισορροπίας.</span></div>
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<strong><span style="color: red; font-family: "verdana" , sans-serif;">ΜΕΤΡΗΣΗ ΤΗΣ ΑΤΜΟΣΦΑΙΡΙΚΗΣ ΠΙΕΣΗΣ</span></strong></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"> Η ατμοσφαιρική πίεση μετρήθηκε για πρώτη φορά το <b>1643</b> από το μαθητή του <b>Γαλιλαίου,</b>τον <b>Ιταλό</b> μαθηματικό και φυσικό <b>Εβαγγελίστα Τορικέλι.</b>Ο </span><span style="font-family: "verdana" , sans-serif;"><b>Τορικέλι </b>για να μετρήσει την ατμοσφαιρική πίεση έκανε ένα πείραμα,που έγινε γνωστό ως πείραμα του </span><span style="font-family: "verdana" , sans-serif;"><b>Τορικέλι.</b></span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkEo7Rin0pQcqGMwtmwQJ8_QTO-XKKkjpTh5BNYJu7xkFrMGawCyQTIpfmfHjmsAFcpXZppL5yaAtTh-eJoyCbboqf5LMYy515IqV2twEgvb0da4zc7xGUe9LuOctFmzyDkxQnhyDNaPV-/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(162).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkEo7Rin0pQcqGMwtmwQJ8_QTO-XKKkjpTh5BNYJu7xkFrMGawCyQTIpfmfHjmsAFcpXZppL5yaAtTh-eJoyCbboqf5LMYy515IqV2twEgvb0da4zc7xGUe9LuOctFmzyDkxQnhyDNaPV-/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(162).JPG" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><span style="line-height: 16px; text-align: justify;">Ο Ιταλός μαθηματικός και φυσικός Εβαγγελίστα Τορικέλι</span> (1608-1647)</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Γεμίζουμε με υδράργυρο ένα γυάλινο σωλήνα που έχει μήκος <b>1 m</b> περίπου,κλείνουμε το στόμιο του με το δάκτυλό μας και το αναποδογυρίζουμε σε μία μικρή λεκάνη με υδράργυρο,φροντίζοντας να φέρουμε το στόμιο του κάτω από την επιφάνεια του υδραργύρου.</span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg1clTNeh-DssVaIsm_DFYDLOcG8rX8Ezb52rFrjlEV_ePdbAkrAdCpIAmB43PhyphenhyphenBSZ2xD0UrJW9cKEVsJeBSmGG0uRusX6IYMi6NL9v8x2YAmwnVMAw5AbpfAEsaR2uQh21N4XjG-oAH8/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(163).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg1clTNeh-DssVaIsm_DFYDLOcG8rX8Ezb52rFrjlEV_ePdbAkrAdCpIAmB43PhyphenhyphenBSZ2xD0UrJW9cKEVsJeBSmGG0uRusX6IYMi6NL9v8x2YAmwnVMAw5AbpfAEsaR2uQh21N4XjG-oAH8/s320/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(163).JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Γεμίζουμε με υδράργυρο ένα γυάλινο σωλήνα που έχει μήκος 1 m περίπου,κλείνουμε το στόμιο του με το δάκτυλό μας και το αναποδογυρίζουμε σε μία μικρή λεκάνη με υδράργυρο</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Μετά αποσύρουμε το δάκτυλό μας και παρατηρούμε ότι ο υδράργυρος κατεβαίνει και σταθεροποιείται σε ορισμένη στάθμη που βρίσκεται σε ύψος <b>h </b>πάνω από την επιφάνεια του υδραργύρου της λεκάνης.Γέρνουμε λίγο το σωλήνα και παρατηρούμε ότι η στάθμη παραμένει διαρκώς στο ίδιο ύψος<b> h.<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdEmVtk2NYTDJc-pJoGhUWb1ZMAXMijgaiBvKu8JsaNJiUUFl50jWvwV7n0c9Tx-GFAuQ5HDBk5kNmhyliB9IC7IqqKxmy_0gZIshrbFcLYeakbwrkeOCEAuvr9TXRDDrXh0RPADzJzjw/s1600/%25CE%25B1%25CE%25B1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdEmVtk2NYTDJc-pJoGhUWb1ZMAXMijgaiBvKu8JsaNJiUUFl50jWvwV7n0c9Tx-GFAuQ5HDBk5kNmhyliB9IC7IqqKxmy_0gZIshrbFcLYeakbwrkeOCEAuvr9TXRDDrXh0RPADzJzjw/s1600/%25CE%25B1%25CE%25B1.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b style="text-align: justify;"><span style="color: purple; font-size: small;">Γέρνουμε λίγο το σωλήνα και παρατηρούμε ότι η στάθμη παραμένει διαρκώς στο ίδιο ύψος h</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Το πείραμα αυτό αποτελείται μία ακόμη απόδειξη για την ύπαρξη ατμοσφαιρικής πίεσης.Ο γύρω αέρας πιέζει την επιφάνεια του υδραργύρου της λεκάνης και συγκρατεί τον υδράργυρο μέσα στο σωλήνα σε κάποιο ύψος <b>h</b>.Αν το πείραμα γίνεται στην επιφάνεια της θάλασσας το ύψος<b> h</b> βρίσκεται ότι είναι <b>76 cm.</b></span></div>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqd-hWeuUOlE7rpVG3TKDZ1Yo_7GgyWGl4AfR5Cj5Ed43J1umOTS3WM2fbwfT6-URVugVaRN-xnDtUFsL2PAArbdE7_bJbNgxzH6UsJR3S2s1ym3-rJ2JtwCJ8ji6Z5Boa2K4QA9OYimg/s1600/%25CE%2591%25CE%25A4%25CE%259C%25CE%259F%25CE%25A3%25CE%25A6%25CE%2591%25CE%2599%25CE%25A1%25CE%2599%25CE%259A%25CE%259F%25CE%25A3+%25CE%2591%25CE%2595%25CE%25A1%25CE%2591%25CE%25A3%25282%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqd-hWeuUOlE7rpVG3TKDZ1Yo_7GgyWGl4AfR5Cj5Ed43J1umOTS3WM2fbwfT6-URVugVaRN-xnDtUFsL2PAArbdE7_bJbNgxzH6UsJR3S2s1ym3-rJ2JtwCJ8ji6Z5Boa2K4QA9OYimg/s1600/%25CE%2591%25CE%25A4%25CE%259C%25CE%259F%25CE%25A3%25CE%25A6%25CE%2591%25CE%2599%25CE%25A1%25CE%2599%25CE%259A%25CE%259F%25CE%25A3+%25CE%2591%25CE%2595%25CE%25A1%25CE%2591%25CE%25A3%25282%2529.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Το πείραμα του Τορικέλι</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Το υγρό μέσα στο σωλήνα και τη λεκάνη ισορροπεί,άρα σύμφωνα με την αρχή των συγκοινωνούντων δοχείων θα ισχύει:</span></div>
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<strong><span style="font-family: "verdana" , sans-serif;"> P<span style="font-size: x-small;">A</span>=P<span style="font-size: x-small;">Β</span></span></strong></div>
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<span style="font-family: "verdana" , sans-serif;">διότι τα <b>Β,Α</b> είναι σημεία του ίδιου υγρού και βρίσκονται στο ίδιο οριζόντιο επίπεδο.</span><br />
<span style="font-family: "verdana" , sans-serif;"> Η πίεση στο <b>Α</b> ισούται με την ατμοσφαιρική πίεση:</span></div>
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<strong><span style="font-family: "verdana" , sans-serif;"> </span></strong><strong><span style="font-family: "verdana" , sans-serif;">P<span style="font-size: x-small;">A</span>=P<span style="font-size: x-small;">atm </span></span></strong></div>
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<span style="font-family: "verdana" , sans-serif;"> Επομένως,η στήλη του υδραργύρου συγκρατείται από τη δύναμη που ασκείται,λόγω της ατμοσφαιρικής πίεσης,στην ελεύθερη επιφάνεια του υδραργύρου της λεκάνης.Μέσα στο σωλήνα πάνω από τη στήλη του υδραργύρου δημιουργήθηκε κενό.</span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPEWSHeu0Btvz6p_Xl7jujv3FbN0Hw83u1yHhjEpjVsE7eKUsSKAfVjg_xj4yyOL5dZzAl0VfU0256U7DLAizW_Y2PiGkqWsH5Dz-93uJdmTD0UBvPZSeF8ASdX2oRfEZyaKUgEjP94qor/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(166).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPEWSHeu0Btvz6p_Xl7jujv3FbN0Hw83u1yHhjEpjVsE7eKUsSKAfVjg_xj4yyOL5dZzAl0VfU0256U7DLAizW_Y2PiGkqWsH5Dz-93uJdmTD0UBvPZSeF8ASdX2oRfEZyaKUgEjP94qor/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(166).JPG" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Η πίεση στο Α είναι ίση με την πίεση στο Β</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Η πίεση στην επιφάνεια της στήλης είναι ίση με το μηδέν και συνεπώς η πίεση στο<b> Β</b> ισούται με την υδροστατική πίεση της στήλης του υδραργύρου:</span></div>
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<strong><span style="font-family: "verdana" , sans-serif;"> </span></strong><strong><span style="font-family: "verdana" , sans-serif;">Ρ<span style="font-size: x-small;">Β</span>=Ρ<span style="font-size: x-small;">υδρ</span></span></strong></div>
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<span style="font-family: "verdana" , sans-serif;"> Συγκρίνουμε τις τελευταίες σχέσεις και συμπεραίνουμε ότι η ατμοσφαιρική πίεση είναι ίση με την πίεση που ασκεί στη βάση της στήλη υδραργύρου ύψους <b>h.</b><span style="text-align: -webkit-auto;">Σύμφωνα με την ισορροπία δυνάμεων όπου η συνολική δύναμη που δέχεται ο υδράργυρος από την ατμόσφαιρα ισούται με το βάρος του υδραργύρου που βρίσκεται πάνω από την επιφάνεια του υδραργύρου την λεκάνη στον δοκιμαστικό σωλήνα.Έτσι,απέδειξε ότι υπάρχει ατμοσφαιρική πίεση.</span>Όταν <b>h=76 cm </b>ή <b>760 mm,</b>λέμε ότι η ατμοσφαιρική πίεση ισούται με <b>760 mmHg.</b> </span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFGqlSxnAI-HYqH1ygQv9k6FSkIYlze4i-Tbk6mNHyTqTnmTLbgdQKYQEbNCbGrTXP-p1A44l1RN1-3J421PwjXwunHphZZ6LKQwFa20Q9bJMR1pLIZU9eGh40R4ibc7VKbNySimXCchr1/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(167).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="196" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFGqlSxnAI-HYqH1ygQv9k6FSkIYlze4i-Tbk6mNHyTqTnmTLbgdQKYQEbNCbGrTXP-p1A44l1RN1-3J421PwjXwunHphZZ6LKQwFa20Q9bJMR1pLIZU9eGh40R4ibc7VKbNySimXCchr1/s200/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(167).JPG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Τη στήλη υδραργύρου ύψους 1mm την ονομάζουμε 1 Torr προς τιμή του Τορικέλι</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Την υδροστατική πίεση που ασκεί στήλη υδραργύρου ύψους <b>1mm</b> την ονομάζουμε<b> 1 Torr </b>προς τιμή του <b>Τορικέλι.</b>Επομένως μπορούμε να πούμε ότι η ατμοσφαιρική πίεση είναι <b>760 Torr.</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"> <span style="text-align: -webkit-auto;">Με το πείραμα του ο <b>Τορικέλι</b> όχι μόνο απέδειξε την ύπαρξη της ατμοσφαιρικής πίεσης </span><span style="text-align: -webkit-auto;">αλλά και την υπολόγισε κιόλας.Σημειώνουμε εδώ ότι στο χώρο πάνω από την επιφάνεια του υδραργύρου μέσα στο σωλήνα δεν υπάρχει αέρας,ο χώρος είναι κενός και επομένως η πίεση στο χώρο αυτό είναι μηδενική.</span></span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS3-puvj-FEdDvjHzkF_bR9A12yk70vbYAPtoWPY4twA9Sxz8PFrRabnG4BWVzHFX_sOXddJ3JOECjH2XAZFX82TSHoo_Id73s4P5Idpr9ZiaLt6CYFUvMKL6u7DFZG_Hwk6F8xZhyphenhyphensbCw/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(164).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS3-puvj-FEdDvjHzkF_bR9A12yk70vbYAPtoWPY4twA9Sxz8PFrRabnG4BWVzHFX_sOXddJ3JOECjH2XAZFX82TSHoo_Id73s4P5Idpr9ZiaLt6CYFUvMKL6u7DFZG_Hwk6F8xZhyphenhyphensbCw/s1600/%CE%A6%CE%A5%CE%A3%CE%99%CE%9A%CE%97+%CE%92+%CE%93%CE%A5%CE%9C%CE%9D%CE%91%CE%A3%CE%99%CE%9F%CE%A5(164).JPG" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="color: purple; font-size: small;"><b style="line-height: 16px; text-align: justify;"><span style="font-family: "verdana" , sans-serif;">Βαρόμετρο είναι ειδικό όργανο μέτρησης της ατμοσφαιρικής πίεσης </span></b> </span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Τα όργανα που χρησιμοποιούνται για τη μέτρηση της ατμοσφαιρικής πίεσης ονομάζονται <strong>βαρόμετρα</strong>.Το πρώτο βαρόμετρο κατασκευάστηκε από τον <b>Τορικέλι.</b></span><br />
<b><span style="font-family: "verdana" , sans-serif;"> <span style="color: blue;">Βαρόμετρο</span> είναι ειδικό όργανο μέτρησης της ατμοσφαιρικής πίεσης</span></b></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-47016350643896327542016-11-10T18:28:00.003-08:002020-09-12T09:54:53.254-07:00ΕΙΔΙΚΗ ΥΓΡΑΣΙΑ ΤΟΥ ΑΕΡΑ<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="background-color: white; color: red; font-family: verdana, sans-serif; text-align: justify;"><span style="font-size: x-large;">ΕΙΔΙΚΗ ΥΓΡΑΣΙΑ ΤΟΥ ΑΕΡΑ</span></b><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs0H92llbeo-7yssZU-Bcpdu5CYUvmRRHBg3cRUlN6ZATUxrj_CXdewbVTuUrlDliP3YAE0Jev04GsUAaLbtZ186QFvCYawlTTEMxay55h1HeYOkka9Fq6C1Yc4Ws82Ctb1YFmpVfnavs/s1600/hygrometry.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs0H92llbeo-7yssZU-Bcpdu5CYUvmRRHBg3cRUlN6ZATUxrj_CXdewbVTuUrlDliP3YAE0Jev04GsUAaLbtZ186QFvCYawlTTEMxay55h1HeYOkka9Fq6C1Yc4Ws82Ctb1YFmpVfnavs/s1600/hygrometry.gif" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b style="background-color: white; font-family: verdana, sans-serif; text-align: justify;"><span style="color: purple; font-size: large;">ΕΙΔΙΚΗ ΥΓΡΑΣΙΑ ΤΟΥ ΑΕΡΑ</span></b></td></tr>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΕΙΣΑΓΩΓΗ</b></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><br /></span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b><span style="color: blue;">Υγρομετρία</span> ονομάζεται το σύνολο των μέσων και των ενεργειών που χρησιμοποιούνται για τον καθορισμό της περιεκτικότητας της ατμόσφαιρας σε υδρατμούς.</b></span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7-R4QxJ6Erj4L2AdpDJYXES07QaSLT34N2Tbsmfr-UCuqsXSBfCoDDwlfCUgJi8xMCesHRNOK0s40KrQYUoZE-d4VH2jXqNxurHYXiKqCZdocd1MNSl9RC2lsxBHrFrU7biUuDCiXIbc/s1600/%25CE%259A%25CE%259B%25CE%2599%25CE%259C%25CE%2591%25CE%25A4%25CE%259F%25CE%259B%25CE%259F%25CE%2593%25CE%2599%25CE%2591%252830%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7-R4QxJ6Erj4L2AdpDJYXES07QaSLT34N2Tbsmfr-UCuqsXSBfCoDDwlfCUgJi8xMCesHRNOK0s40KrQYUoZE-d4VH2jXqNxurHYXiKqCZdocd1MNSl9RC2lsxBHrFrU7biUuDCiXIbc/s400/%25CE%259A%25CE%259B%25CE%2599%25CE%259C%25CE%2591%25CE%25A4%25CE%259F%25CE%259B%25CE%259F%25CE%2593%25CE%2599%25CE%2591%252830%2529.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; text-align: justify;">Υγρομετρία ονομάζεται το σύνολο των μέσων και των ενεργειών που χρησιμοποιούνται για τον καθορισμό της περιεκτικότητας της ατμόσφαιρας σε υδρατμούς</span></span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Η υγρομετρία είναι αντικείμενο της μετεωρολογίας.Η εξάτμιση λόγω θερμότητας των νερών των θαλασσών,των λιμνών,των ελών κτλ. έχει ως αποτέλεσμα τον εμπλουτισμό του ατμοσφαιρικού αέρα με υδρατμούς,των οποίων η ποσότητα είναι συνάρτηση ορισμένων παραγόντων.</span><br />
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<b style="background-color: white; color: red; font-family: verdana, sans-serif;">ΕΙΔΙΚΗ ΥΓΡΑΣΙΑ ΤΟΥ ΑΕΡΑ</b></div>
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<span style="font-family: "verdana" , sans-serif;"><b><br /></b></span><b style="background-color: transparent; font-family: verdana, sans-serif;"><span style="color: blue;"> </span><span style="color: blue;">Ειδική υγρασία του αέρα </span>λέγεται το βάρος των υδρατμών σε γραμμάρια που περιέχεται σε 1 κιλό μείγματος ξηρού αέρα και υδρατμών.</b><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQPDiKsg-O9KKPrGKtpHM7IiMWIme0J-6rEDj9GNi3hRT-HIHrOqA7X0LmzOKCjQRU7_7oEUbenThGqKe1XmXTn0o4IUNUYu_I7N4DCOGFAii4CxUP-x5TKloyG7MUJJlJ8Q3vKhrZeWQ/s1600/%25CE%2591%25CE%25A0%25CE%259F%25CE%259B%25CE%25A5%25CE%25A4%25CE%2597+%25CE%25A5%25CE%2593%25CE%25A1%25CE%2591%25CE%25A3%25CE%2599%25CE%2591+%25CE%25A4%25CE%259F%25CE%25A5+%25CE%2591%25CE%2595%25CE%25A1%25CE%2591.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQPDiKsg-O9KKPrGKtpHM7IiMWIme0J-6rEDj9GNi3hRT-HIHrOqA7X0LmzOKCjQRU7_7oEUbenThGqKe1XmXTn0o4IUNUYu_I7N4DCOGFAii4CxUP-x5TKloyG7MUJJlJ8Q3vKhrZeWQ/s1600/%25CE%2591%25CE%25A0%25CE%259F%25CE%259B%25CE%25A5%25CE%25A4%25CE%2597+%25CE%25A5%25CE%2593%25CE%25A1%25CE%2591%25CE%25A3%25CE%2599%25CE%2591+%25CE%25A4%25CE%259F%25CE%25A5+%25CE%2591%25CE%2595%25CE%25A1%25CE%2591.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="background-color: transparent; font-family: verdana, sans-serif; text-align: justify;"><span style="color: purple; font-size: small;"><span style="color: blue;">Ειδική υγρασία του αέρα </span>λέγεται το βάρος των υδρατμών σε γραμμάρια που περιέχεται σε 1 κιλό μείγματος ξηρού αέρα και υδρατμών</span></b></td></tr>
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<span style="background-color: transparent;"><span style="font-family: "verdana" , sans-serif;"><b> </b></span></span><b style="background-color: transparent; font-family: verdana, sans-serif;"><span style="color: blue;">Ειδική υγρασία του αέρα </span></b><b style="background-color: transparent; font-family: verdana, sans-serif;"><span style="color: red;">q</span> ονομάζεται τ</b><b style="background-color: transparent; font-family: verdana, sans-serif;">ο πηλίκο της μάζας των υδρατμών Μv προς τη μάζα του υγρού αέρα Μ<span style="font-size: x-small;">v</span>+M<span style="font-size: x-small;">d</span> που τους περιέχει.</b><br />
<b style="background-color: transparent; font-family: verdana, sans-serif;"><br /></b><b style="background-color: transparent; font-family: verdana, sans-serif;"><i> </i><span style="color: red;"><b> </b></span><span style="color: red;">q=</span></b><span style="color: red;"><b style="background-color: transparent; font-family: verdana, sans-serif;">Μ<span style="font-size: x-small;">v</span>/</b><b style="background-color: transparent; font-family: verdana, sans-serif;">Μ<span style="font-size: x-small;">v</span>+M<span style="font-size: x-small;">d</span></b></span><br />
<b style="background-color: transparent; font-family: verdana, sans-serif;"><br /></b><span style="background-color: transparent; font-family: "verdana" , sans-serif;"> </span><span style="font-family: "verdana" , sans-serif;">Η ειδική υγρασία είναι μια εξαιρετική χρήσιμη ποσότητα στη μετεωρολογία.Για παράδειγμα,η ταχύτητα εξάτμισης του νερού από οποιαδήποτε επιφάνεια είναι ευθέως ανάλογη με τη συγκεκριμένη διαφορά υγρασίας μεταξύ της επιφάνειας και του αέρα.</span><br />
<span style="font-family: "verdana" , sans-serif;"> Επιπλέον,η ειδική υγρασία δεν μεταβάλλεται με τη θερμοκρασία ή τη πίεση του σώματος.Αυτή η σταθερότητα της συγκεκριμένης υγρασίας τη καθιστά χρήσιμη σαν αναγνωριστική ιδιότητα μιας κινούμενης μάζας αέρα.Η ειδική υγρασία του κορεσμένου αέρα αυξάνει ταχέως με την αύξηση της θερμοκρασίας.</span></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-140325262387442742016-11-10T18:26:00.003-08:002020-09-12T09:54:53.449-07:00ΑΠΟΛΥΤΗ ΥΓΡΑΣΙΑ ΤΟΥ ΑΕΡΑ<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="color: red; font-family: verdana, sans-serif; text-align: justify;"><span style="font-size: x-large;">ΑΠΟΛΥΤΗ ΥΓΡΑΣΙΑ ΤΟΥ ΑΕΡΑ<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPmzPxLIOoF8Rl_ileekhqUuwTQvI9Z1eNd6cU6wGCXRJZkfucMDVoNa1NYm-SCDbEh_WcLUAequyZF-rtSqYwP_3YR0lhTnEWqI7r8qcYLJLfXqKD8v-0A31cyaQg0A8fmmTev08GsR8/s1600/HUMIDITY.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPmzPxLIOoF8Rl_ileekhqUuwTQvI9Z1eNd6cU6wGCXRJZkfucMDVoNa1NYm-SCDbEh_WcLUAequyZF-rtSqYwP_3YR0lhTnEWqI7r8qcYLJLfXqKD8v-0A31cyaQg0A8fmmTev08GsR8/s1600/HUMIDITY.gif" /></a></td></tr>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΕΙΣΑΓΩΓΗ</b></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><br /></span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b><span style="color: blue;">Υγρομετρία</span> ονομάζεται το σύνολο των μέσων και των ενεργειών που χρησιμοποιούνται για τον καθορισμό της περιεκτικότητας της ατμόσφαιρας σε υδρατμούς.</b></span><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7-R4QxJ6Erj4L2AdpDJYXES07QaSLT34N2Tbsmfr-UCuqsXSBfCoDDwlfCUgJi8xMCesHRNOK0s40KrQYUoZE-d4VH2jXqNxurHYXiKqCZdocd1MNSl9RC2lsxBHrFrU7biUuDCiXIbc/s1600/%25CE%259A%25CE%259B%25CE%2599%25CE%259C%25CE%2591%25CE%25A4%25CE%259F%25CE%259B%25CE%259F%25CE%2593%25CE%2599%25CE%2591%252830%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7-R4QxJ6Erj4L2AdpDJYXES07QaSLT34N2Tbsmfr-UCuqsXSBfCoDDwlfCUgJi8xMCesHRNOK0s40KrQYUoZE-d4VH2jXqNxurHYXiKqCZdocd1MNSl9RC2lsxBHrFrU7biUuDCiXIbc/s320/%25CE%259A%25CE%259B%25CE%2599%25CE%259C%25CE%2591%25CE%25A4%25CE%259F%25CE%259B%25CE%259F%25CE%2593%25CE%2599%25CE%2591%252830%2529.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; text-align: justify;">Υγρομετρία ονομάζεται το σύνολο των μέσων και των ενεργειών που χρησιμοποιούνται για τον καθορισμό της περιεκτικότητας της ατμόσφαιρας σε υδρατμούς</span></span></b></td></tr>
</tbody></table>
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Η υγρομετρία είναι αντικείμενο της μετεωρολογίας.Η εξάτμιση λόγω θερμότητας των νερών των θαλασσών,των λιμνών,των ελών κτλ. έχει ως αποτέλεσμα τον εμπλουτισμό του ατμοσφαιρικού αέρα με υδρατμούς,των οποίων η ποσότητα είναι συνάρτηση ορισμένων παραγόντων.</span></div>
</div>
<div style="line-height: 16px; padding: 0px;">
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;"><b><br /></b></span><span style="color: red; font-family: "verdana" , sans-serif;"><b>ΑΠΟΛΥΤΗ ΥΓΡΑΣΙΑ ΤΟΥ ΑΕΡΑ</b></span><br />
<span style="font-family: "verdana" , sans-serif;"><br /></span>
<span style="font-family: "verdana" , sans-serif;"><span style="color: red;"><b> </b></span>Όταν επικρατεί ομίχλη ο αέρας είναι συνήθως κεκορεσμένος.Ιδιαίτερης σημασίας είναι το γεγονός ότι:όταν η θερμοκρασία αέρος,που περιέχει ορισμένη ποσότητα υδρατμών ελαττώνεται,η σχετική υγρασία του αυξάνει και αντίστροφα.Πολύ συχνά τα </span><b style="font-family: verdana, sans-serif;">Δελτία καιρού </b><span style="font-family: "verdana" , sans-serif;">αναφέρουν και το στοιχείο της "σχετικής υγρασίας" σε ποσοστό επί τοις </span><b style="font-family: verdana, sans-serif;">100,</b><span style="font-family: "verdana" , sans-serif;">π.χ. </span><b style="font-family: verdana, sans-serif;">50%,60% </b><span style="font-family: "verdana" , sans-serif;">κ.λπ.Όταν η σχετική υγρασία είναι </span><b style="font-family: verdana, sans-serif;">100%</b><span style="font-family: "verdana" , sans-serif;"> τότε η ατμόσφαιρα είναι κεκορεσμένη δηλαδή πλήρης υδρατμών μη δυνάμενη να συγκρατήσει άλλους.Αντίθετα όταν είναι π.χ. </span><b style="font-family: verdana, sans-serif;">50%</b><span style="font-family: "verdana" , sans-serif;"> και η θερμοκρασία αέρος</span><b style="font-family: verdana, sans-serif;"> 20° C </b><span style="font-family: "verdana" , sans-serif;">για τον </span><b style="font-family: verdana, sans-serif;">Χειμωνα</b><span style="font-family: "verdana" , sans-serif;">,και </span><b style="font-family: verdana, sans-serif;">26° C </b><span style="font-family: "verdana" , sans-serif;">για το Καλοκαίρι,τότε αισθανόμαστε ευχάριστα.</span><br />
<div style="padding: 0px;">
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMmNzb0qqvMM31dsn-qW37On2iONizEW6nStYNrWOppUZjD4gKA18zZE11sPtkl992_euwlnJCfcsFMdBT4wDrhxENK_INfm9b8uTvDbUcC8m2WV1SJGjBY3rUxe9F_8x9wmdB8SIEtog/s1600/%25CE%2591%25CE%25A0%25CE%259F%25CE%259B%25CE%25A5%25CE%25A4%25CE%2597+%25CE%25A5%25CE%2593%25CE%25A1%25CE%2591%25CE%25A3%25CE%2599%25CE%2591+%25CE%25A4%25CE%259F%25CE%25A5+%25CE%2591%25CE%2595%25CE%25A1%25CE%25914.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMmNzb0qqvMM31dsn-qW37On2iONizEW6nStYNrWOppUZjD4gKA18zZE11sPtkl992_euwlnJCfcsFMdBT4wDrhxENK_INfm9b8uTvDbUcC8m2WV1SJGjBY3rUxe9F_8x9wmdB8SIEtog/s320/%25CE%2591%25CE%25A0%25CE%259F%25CE%259B%25CE%25A5%25CE%25A4%25CE%2597+%25CE%25A5%25CE%2593%25CE%25A1%25CE%2591%25CE%25A3%25CE%2599%25CE%2591+%25CE%25A4%25CE%259F%25CE%25A5+%25CE%2591%25CE%2595%25CE%25A1%25CE%25914.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="color: purple; font-size: small;"><span class="Apple-style-span" style="font-family: "verdana" , sans-serif; text-align: justify;"><b><span style="color: blue;">Απόλυτη υγρασία του αέρα</span> λέγεται το ποσό των υδρατμών σε γραμμάρια</b></span><span style="font-family: "verdana" , sans-serif; text-align: justify;"><b><span style="background-color: white; line-height: 19px; text-align: -webkit-auto;">(gr)</span>,το οποίο περιέχεται σ’ ένα κυβικό μέτρο (<span style="background-color: white; line-height: 19px; text-align: -webkit-auto;">1 m</span><sup style="background-color: white; line-height: 19px; text-align: -webkit-auto;">3</sup>) ατμοσφαιρικού αέρα</b></span></span></td></tr>
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</div>
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<div style="padding: 0px;">
<div style="text-align: justify;">
<div style="line-height: 16px;">
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span style="color: blue;"> </span><span style="color: blue;">Απόλυτη υγρασία του αέρα</span> λέγεται το ποσό των υδρατμών σε γραμμάρια</b></span><span style="font-family: "verdana" , sans-serif;"><b><span style="background-color: white; line-height: 19px; text-align: -webkit-auto;">(gr)</span>,το οποίο περιέχεται σ’ ένα κυβικό μέτρο (<span style="background-color: white; line-height: 19px; text-align: -webkit-auto;">1 m</span><sup style="background-color: white; line-height: 19px; text-align: -webkit-auto;">3</sup>) ατμοσφαιρικού αέρα.</b></span></div>
<div style="line-height: 16px;">
<span style="background-color: white; line-height: 19px; text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;"><b> </b>Από τον ορισμό καταλαβαίνουμε ότι πρόκειται για την πυκνότητα του αέρα σε υδρατμούς.</span></span><br />
<span style="background-color: white; line-height: 19px; text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;"> Υπολογίζεται από τον τύπο:</span></span></div>
<div style="line-height: 16px;">
</div>
<div style="background-color: white; line-height: 19px; text-align: center;">
<div style="line-height: 1.5em; margin-bottom: 0.5em; margin-top: 0.4em; text-align: justify;">
<span class="texhtml" dir="ltr"><span style="font-family: "verdana" , sans-serif;"><i> </i><span style="color: red;"><b> a</b></span><span style="color: red;"><b>=m/V</b></span></span></span></div>
</div>
<div style="background-color: white; line-height: 19px; margin-bottom: 0.5em; margin-top: 0.4em;">
<span style="font-family: "verdana" , sans-serif;"> Η ικανότητα του αέρα να συγκρατεί μικρή ή μεγάλη ποσότητα υδρατμών είναι ανάλογη προς την θερμοκρασία του.Σε μία συγκεκριμένη θερμοκρασία η ποσότητα των υδρατμών που μπορεί να συγκρατήσει η ατμόσφαιρά έχει μια μέγιστη τιμή.Την τιμή αυτή μπορούμε να την υπολογίσουμε από την εξίσωση των <b>Magnus-Tetens</b>,όπου <b>θ</b> η θερμοκρασία που έχει η ατμόσφαιρα μετρούμενη σε <b>βαθμούς Κελσίου (<sup>ο</sup>C).</b></span></div>
</div>
</div>
</div>
ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-23863371205973311722016-11-10T18:24:00.000-08:002020-09-12T09:54:53.644-07:00ΣΧΕΤΙΚΗ ΥΓΡΑΣΙΑ ΤΟΥ ΑΕΡΑ<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="color: red; font-family: "verdana" , sans-serif; font-size: x-large;"><b>ΣΧΕΤΙΚΗ ΥΓΡΑΣΙΑ ΤΟΥ ΑΕΡΑ</b></span></div>
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<div style="text-align: justify;">
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTvTRJkJ7sr4pQoKI0tVhXQHv2h5ULu0Xhiv1Zf6SLhz7v2L-0ilQ9KHhiJR7BTy_30hj8gRGf827aBpQZmNSyj_e_VW0bRXMjKoNPHIfEB8GSBd5jbJAw7HoXe8KOVwpwtHyW9lccJEI/s1600/%25CE%25A3%25CE%25A7%25CE%2595%25CE%25A4%25CE%2599%25CE%259A%25CE%2597+%25CE%25A5%25CE%2593%25CE%25A1%25CE%2591%25CE%25A3%25CE%2599%25CE%2591+%25CE%25A4%25CE%259F%25CE%25A5+%25CE%2591%25CE%2595%25CE%25A1%25CE%2591.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTvTRJkJ7sr4pQoKI0tVhXQHv2h5ULu0Xhiv1Zf6SLhz7v2L-0ilQ9KHhiJR7BTy_30hj8gRGf827aBpQZmNSyj_e_VW0bRXMjKoNPHIfEB8GSBd5jbJAw7HoXe8KOVwpwtHyW9lccJEI/s320/%25CE%25A3%25CE%25A7%25CE%2595%25CE%25A4%25CE%2599%25CE%259A%25CE%2597+%25CE%25A5%25CE%2593%25CE%25A1%25CE%2591%25CE%25A3%25CE%2599%25CE%2591+%25CE%25A4%25CE%259F%25CE%25A5+%25CE%2591%25CE%2595%25CE%25A1%25CE%2591.gif" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><div style="text-align: justify;">
<span style="color: purple; font-family: "verdana" , sans-serif; font-size: large;"><b>ΣΧΕΤΙΚΗ ΥΓΡΑΣΙΑ ΤΟΥ ΑΕΡΑ</b></span></div>
<div>
<span style="color: red; font-family: "verdana" , sans-serif;"><b><br /></b></span></div>
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<span class="Apple-style-span" style="color: red; font-family: "verdana" , sans-serif;"><b>ΕΙΣΑΓΩΓΗ</b></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><br /></span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b><span style="color: blue;">Υγρομετρία</span> ονομάζεται το σύνολο των μέσων και των ενεργειών που χρησιμοποιούνται για τον καθορισμό της περιεκτικότητας της ατμόσφαιρας σε υδρατμούς.</b></span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7-R4QxJ6Erj4L2AdpDJYXES07QaSLT34N2Tbsmfr-UCuqsXSBfCoDDwlfCUgJi8xMCesHRNOK0s40KrQYUoZE-d4VH2jXqNxurHYXiKqCZdocd1MNSl9RC2lsxBHrFrU7biUuDCiXIbc/s1600/%25CE%259A%25CE%259B%25CE%2599%25CE%259C%25CE%2591%25CE%25A4%25CE%259F%25CE%259B%25CE%259F%25CE%2593%25CE%2599%25CE%2591%252830%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7-R4QxJ6Erj4L2AdpDJYXES07QaSLT34N2Tbsmfr-UCuqsXSBfCoDDwlfCUgJi8xMCesHRNOK0s40KrQYUoZE-d4VH2jXqNxurHYXiKqCZdocd1MNSl9RC2lsxBHrFrU7biUuDCiXIbc/s320/%25CE%259A%25CE%259B%25CE%2599%25CE%259C%25CE%2591%25CE%25A4%25CE%259F%25CE%259B%25CE%259F%25CE%2593%25CE%2599%25CE%2591%252830%2529.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; text-align: justify;">Υγρομετρία ονομάζεται το σύνολο των μέσων και των ενεργειών που χρησιμοποιούνται για τον καθορισμό της περιεκτικότητας της ατμόσφαιρας σε υδρατμούς</span></span></b></td></tr>
</tbody></table>
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Η υγρομετρία είναι αντικείμενο της μετεωρολογίας.Η εξάτμιση λόγω θερμότητας των νερών των θαλασσών,των λιμνών,των ελών κτλ. έχει ως αποτέλεσμα τον εμπλουτισμό του ατμοσφαιρικού αέρα με υδρατμούς,των οποίων η ποσότητα είναι συνάρτηση ορισμένων παραγόντων.</span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><br /></span><span style="color: red; font-family: "verdana" , sans-serif;"><b>ΣΧΕΤΙΚΗ ΥΓΡΑΣΙΑ ΤΟΥ ΑΕΡΑ</b></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><br /></span><span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Η ποσότητα των υδρατμών δεν μπορεί μόνη της να είναι κριτήριο της υγρομετρικής κατάστασης του ατμοσφαιρικού αέρα.Ως σημείο αναφοράς χρησιμοποιείται η ποσότητα των υδρατμών,η οποία είναι απαραίτητη,ώστε ο αέρας να κορεστεί από υδρατμούς.Αυτό φυσικά εξαρτάται κυρίως από τη θερμοκρασία του ατμοσφαιρικού αέρα και από την ύπαρξη ή όχι ανέμου.Έτσι για τη θερμοκρασία <b>15°C</b> ο κορεσμένος αέρας περιέχει <b>12,78</b> γραμμάρια υδρατμών σε κάθε κυβικό μέτρο.Αν στην ίδια θερμοκρασία ο αέρας περιέχει<b> 6,39</b> γραμμάρια στο κυβικό μέτρο,τότε ο λόγος αν εκφραστεί σε <b>%</b> θα δώσει τη σχετική υγρασία του αέρα,δηλαδή αυτή θα είναι <b>50%.</b></span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTvTRJkJ7sr4pQoKI0tVhXQHv2h5ULu0Xhiv1Zf6SLhz7v2L-0ilQ9KHhiJR7BTy_30hj8gRGf827aBpQZmNSyj_e_VW0bRXMjKoNPHIfEB8GSBd5jbJAw7HoXe8KOVwpwtHyW9lccJEI/s1600/%25CE%25A3%25CE%25A7%25CE%2595%25CE%25A4%25CE%2599%25CE%259A%25CE%2597+%25CE%25A5%25CE%2593%25CE%25A1%25CE%2591%25CE%25A3%25CE%2599%25CE%2591+%25CE%25A4%25CE%259F%25CE%25A5+%25CE%2591%25CE%2595%25CE%25A1%25CE%2591.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTvTRJkJ7sr4pQoKI0tVhXQHv2h5ULu0Xhiv1Zf6SLhz7v2L-0ilQ9KHhiJR7BTy_30hj8gRGf827aBpQZmNSyj_e_VW0bRXMjKoNPHIfEB8GSBd5jbJAw7HoXe8KOVwpwtHyW9lccJEI/s320/%25CE%25A3%25CE%25A7%25CE%2595%25CE%25A4%25CE%2599%25CE%259A%25CE%2597+%25CE%25A5%25CE%2593%25CE%25A1%25CE%2591%25CE%25A3%25CE%2599%25CE%2591+%25CE%25A4%25CE%259F%25CE%25A5+%25CE%2591%25CE%2595%25CE%25A1%25CE%2591.gif" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="text-align: justify;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><span style="color: blue;">Σχετική υγρασία του αέρα</span> ονομάζεται ο λόγος της μάζας των υδρατμών που υπάρχουν σε ορισμένο όγκο αέρα προς τη μάζα των υδρατμών που χρειάζονται,ώστε ο αέρας να γίνει κορεσμένος στην ίδια θερμοκρασία</span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"></span></div>
</div>
<div style="line-height: 16px; padding: 0px;">
<div style="text-align: justify;">
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b><span style="color: blue;">Σχετική υγρασία του αέρα</span> ονομάζεται ο λόγος της μάζας των υδρατμών που υπάρχουν σε ορισμένο όγκο αέρα προς τη μάζα των υδρατμών που χρειάζονται,ώστε ο αέρας να γίνει κορεσμένος στην ίδια θερμοκρασία. </b></span><br />
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;"><span style="text-align: -webkit-auto;"> Η σχετική υγρασία εκφράζεται </span><strong style="text-align: -webkit-auto;">επί τοις %</strong><span style="text-align: -webkit-auto;">.</span></span><br />
<span style="font-family: "verdana" , sans-serif;"> Έτσι έχουμε το τύπο: </span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;"><strong style="text-align: -webkit-auto;"><br /></strong></span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;"><strong style="text-align: -webkit-auto;"> <span style="color: red;"> Συ=Β΄/Β <span style="font-size: x-small;">Χ</span>100</span></strong><span style="text-align: -webkit-auto;"><span style="color: red;"> </span></span></span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">όπου:</span></div>
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<span style="text-align: -webkit-auto;"><span style="color: red; font-family: "verdana" , sans-serif; font-weight: bold;">Β΄</span><span style="background-color: white; font-family: "verdana" , sans-serif;"><b>η</b></span></span><span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;"> </span><span style="color: blue;">ποσότητα υπαρχόντων υδρατμών</span> και</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="text-align: -webkit-auto;"><span style="color: red;">Β </span></span></b></span><b style="font-family: Verdana, sans-serif; text-align: start;">η</b><span style="font-family: "verdana" , sans-serif;"><b><span style="text-align: -webkit-auto;"> <span style="color: blue;">ποσότητα που καθιστά τον αέρα κεκορεσμένο</span> ή </span><span style="text-align: -webkit-auto;">μέγιστη τάση υδρατμών</span><span style="text-align: -webkit-auto;">.</span></b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="text-align: -webkit-auto;"> Ο κεκορεσμένος αέρας έχει </span><span style="text-align: -webkit-auto;">σχετική υγρασία</span><span style="text-align: -webkit-auto;"> <b>100%</b>,ενώ ο τελείως ξηρός αέρας έχει υγρασία <b>0%.</b></span></span></div>
<span style="font-family: "verdana" , sans-serif;"><b> Η σχετική υγρασία παρουσιάζει τόσο ημερήσια όσο και ετήσια κύμανση,ενώ μεταβάλλεται ανάλογα με το ύψος και το γεωγραφικό πλάτος.</b></span><br />
<span style="font-family: "verdana" , sans-serif;"><b> </b></span><span style="font-family: "verdana" , sans-serif;"> Η γνώση της<b> </b></span><span style="font-family: verdana, sans-serif;"><b>σχετικής υγρασίας</b></span><span style="font-family: "verdana" , sans-serif;"><b> </b>παρουσιάζει ιδιαίτερο ενδιαφέρον διότι είναι εκείνη που πληροφορεί για τα υδάτινα ή ατμοσφαιρικά κατακρημνίσματα καθώς και για τις συνθήκες πάγου που κρίνονται επικίνδυνες στις αερομεταφορές.</span></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-48669416856443589582016-11-09T18:40:00.001-08:002020-09-12T09:54:53.840-07:00ΣΚΕΔΑΣΗ COMPTON<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="color: red; font-family: Verdana, sans-serif; line-height: 16px; text-align: justify;"><span style="font-size: x-large;">ΣΚΕΔΑΣΗ COMPTON</span></b><br />
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<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: large;">ΣΚΕΔΑΣΗ COMPTON</span></b></td></tr>
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<strong><span style="color: red; font-family: "verdana" , sans-serif;">ΟΙ ΑΚΤΙΝΕΣ Χ</span></strong></div>
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<span style="font-family: "verdana" , sans-serif;"> Το <b>1895</b> ο <b>Wilchelm Rontgen (Ρέντγκεν) </b>ανακάλυψε ότι όταν ένα μέταλλο «βομβαρδιστεί» με ηλεκτρόνια που κινούνται με μεγάλη ταχύτητα εκπέμπει ηλεκτρομαγνητική ακτινοβολία.Η ακτινοβολία αυτή ονομάστηκε <b>ακτίνες Χ </b>ή <b>ακτίνες Rontgen</b>.<b>Ακτίνες Χ</b> χρησιμοποιούνται καθημερινά σήμερα για την λήψη κοινών ακτινογραφιών.Οι ακτίνες <b>Χ </b>έχουν μήκη κύματος από<b> 0,001 nm,</b>έως <b>1 nm.</b></span><br />
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<strong style="line-height: 16px;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Ο Βίλχελμ Κόνραντ Ρέντγκεν (Wilhelm Conrad Röntgen,27 Μαρτίου 1845-10 Φεβρουαρίου 1923) ήταν Γερμανός φυσικός.Σπούδασε στο ETH Ζυρίχης.Διετέλεσε υφηγητής στο πανεπιστήμιο του Στρασβούργου το 1874,τακτικός καθηγητής της Φυσικής και διευθυντής του εργαστηρίου Φυσικής του πανεπιστημίου Γκίσεν,καθηγητής στο πανεπιστήμιο του Βίρτσμπουργκ το 1885 και τελικά καθηγητής στο πανεπιστήμιο του Μονάχου (1900-1920).Κατά το 1895,ενώ έκανε στο Βίρτσμπουργκ πειράματα για τη σπουδή της ηλεκτρικής αγωγιμότητας των αερίων,ανακάλυψε τις ακτίνες Χ (ή τις ακτίνες Ρέντγκεν, όπως λέγονται εις τιμήν του).Απέδειξε ότι οι ακτίνες Χ διαδίδονται σε ευθεία γραμμή και δεν είναι δυνατό να διαθλαστούν ή να ανακλαστούν και ότι δεν επηρεάζονται από τα ηλεκτρικά μαγνητικά πεδία.Έκανε επίσης μελέτες σχετικές με την ελαστικότητα των σωμάτων,την ειδική θερμότητα των αερίων,τη θερμική αγωγιμότητα των κρυστάλλων,την απορρόφηση των θερμικών ακτίνων από τα αέρια κλπ.Το 1896 τιμήθηκε με το μετάλλιο Ρούμφορ της Βασιλικής Εταιρείας και το 1901 με το βραβείο Νόμπελ Φυσικής</span></strong></div>
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<span style="font-family: "verdana" , sans-serif;"> Ο μηχανισμός παραγωγής των <b>ακτίνων Χ</b> είναι ακριβώς ο αντίστροφος του φωτοηλεκτρικού φαινομένου.Στο φωτοηλεκτρικό φαινόμενο μια μεταλλική επιφάνεια «βομβαρδίζεται» με ηλεκτρομαγνητικό κύμα και εκπέμπει ηλεκτρόνια.Στις<b> ακτίνες Χ </b>η μεταλλική επιφάνεια «βομβαρδίζεται» με ηλεκτρόνια και εκπέμπει ηλεκτρομαγνητικό κύμα.</span></div>
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<span style="font-family: "verdana" , sans-serif;"> Όταν τα ηλεκτρόνια της δέσμης φτάνουν στην επιφάνεια του μετάλλου επιβραδύνονται απότομα.Η επιβράδυνση αυτή συνοδεύεται από εκπομπή ακτινοβολίας,το φωτόνιο της οποίας θα έχει ενέργεια μικρότερη ή ίση με την ενέργεια του ηλεκτρονίου στο οποίο οφείλεται η εκπομπή του.</span></div>
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<span style="font-family: "verdana" , sans-serif;"> Υπάρχει και άλλη αιτία για την οποία εκπέμπεται ακτινοβολία από τη μεταλλική επιφάνεια.Καθώς τα ηλεκτρόνια συγκρούονται με τα άτομα της επιφάνειας του μετάλλου τούς μεταφέρουν ενέργεια.Τα άτομα διεγείρονται,τα ηλεκτρόνιά τους δηλαδή μεταφέρονται σε στιβάδες μεγαλύτερης ενέργειας.Όταν αποδιεγείρονται,όταν δηλαδή τα ηλεκτρόνια επανέλθουν στην αρχική τους στιβάδα,εκπέμπουν στο περιβάλλον ενέργεια υπό μορφή ηλεκτρομαγνητικής ακτινοβολίας.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><strong style="line-height: 16px; text-align: -webkit-auto;"><span style="color: red;">ΣΚΕΔΑΣΗ COMPTON(ΚΟΠΤΟΝ)</span></strong></span></div>
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<span style="font-family: "verdana" , sans-serif;"> Η ύπαρξη φωτονίων επιβεβαιώθηκε πειραματικά το <b>1924</b> από τον <b>Αμερικανό Arthur Holly Compton.</b>Ο <b>Compton </b>παρατήρησε ότι όταν <b>ακτίνες Χ</b> προσπίπτουν πάνω σε μια υλική επιφάνεια ένα μέρος τους εκτρέπεται από τα σωματίδια της ύλης (σκεδάζεται).</span><br />
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<strong style="line-height: 16px;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Ο Άρθουρ Χόλι Κόμπτον (10 Σεπτεμβρίου 1892-15 Μαρτίου 1962) ήταν Αμερικανός φυσικός στον οποίο το 1927 απονεμήθηκε το βραβείο Νόμπελ Φυσικής για την ανακάλυψη του φαινομένου που φέρει το όνομα του.Ο Κόμπτον γεννήθηκε στο Wooster της πολιτείας Οχάιο το 1892 από τον Ελάιας και την Οτέλια Κόμπτον.Ήταν μια ακαδημαϊκή οικογένεια.Ο πατέρας του ήταν πρύτανης του Πανεπιστημίου Wooster το οποίο παρακολούθησε ο Άρτουρ και επίσης έγινε μέλος της Άλφα Ωμέγα Ταυ αδελφότητας.Ο μεγαλύτερος αδελφός του Καρλ σπούδασε επίσης στο Πανεπιστήμιο Wooster,έγινε φυσικός,και αργότερα πρόεδρος του MIT.O δεύτερος αδερφός του Γουίλσον Μάρτιντεϊλ Κόμπτον σπούδασε επίσης στο Πανεπιστήμιο Wooster και έγινε διπλωμάτης και πρόεδρος του State College της Ουάσινγκτον,αργότερα Washington State University.Και τα τρία αδέρφια πήραν το Ph.D. τους από το Πανεπιστήμιο Πρίνστον</span></strong></div>
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<span style="font-family: "verdana" , sans-serif;"> Ο <b>Compton</b> διαπίστωσε ότι το σκεδαζόμενο τμήμα της ακτινοβολίας έχει μήκος κύματος μεγαλύτερο από το μήκος κύματος της προσπίπτουσας ακτινοβολίας (μικρότερη συχνότητα).</span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Το πείραμα του Compton</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Οι μετρήσεις του<b> Compton</b> έδειξαν ότι η μεταβολή του μήκους κύματος ανάμεσα στην προσπίπτουσα και τη σκεδαζόμενη δέσμη εξαρτάται μόνο από τη γωνία ανάμεσα στις δύο δέσμες και μάλιστα υπακούει στη σχέση:</span><br />
<span style="font-family: "verdana" , sans-serif;"><br /></span><b style="font-family: Verdana, sans-serif;"><span style="color: red;"> </span></b><span style="color: red; font-family: "verdana" , sans-serif;"><b>λ'-λ=h/m·c·(1-συνφ)</b></span></div>
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<span style="line-height: 16px; text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;">όπου: </span></span><br />
<span style="line-height: 16px; text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">λ' </span>το<span style="color: blue;"> μήκος κύματος</span> της σκεδαζόμενης δέσμης, </b></span></span><br />
<span style="line-height: 16px; text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">λ</span> το <span style="color: blue;">μήκος κύματος</span> της προσπίπτουσας δέσμης, </b></span></span><br />
<span style="font-family: "verdana" , sans-serif;"><span style="line-height: 16px; text-align: -webkit-auto;"><b><span style="color: red;">m </span>η </b></span><b style="line-height: 16px;"><span style="color: blue;">μάζα</span> </b><b style="line-height: 16px;">του ηλεκτρονίου και </b></span><br />
<span style="line-height: 16px; text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">φ</span> η <span style="color: blue;">γωνία </span>μεταξύ προσπίπτουσας και ανακλώμενης δέσμης.</b></span></span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Η σκέδαση Compton</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Σύμφωνα με την κλασική θεωρία ένα ηλεκτρομαγνητικό κύμα συχνότητας <b> f </b>που προσπίπτει σ' ένα υλικό αναγκάζει τα ηλεκτρόνια του υλικού να ταλαντώνονται με την ίδια συχνότητα και,επακόλουθα,να παράγουν με τη σειρά τους σαν μικρές κεραίες,ηλεκτρομαγνητικό κύμα της ίδιας συχνότητας<b> f.</b>Η κλασική θεωρία,λοιπόν,θα περίμενε η σκεδαζόμενη δέσμη να έχει την ίδια συχνότητα και,αντίστοιχα,ίδιο μήκος κύματος με την προσπίπτουσα δέσμη.</span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii-zEi30SU3U8JJp6VpVnO1UxvBHatWOuos8iV1C8Idl3ikA_kOl3GF40syvuTsAEUTo7aB-oseVhYoV-TRA8HP7DG-fgMfyBwIYKNY1wyyNEbUcFuxJQ-dJ_lj8_VyPmRpWApN8vdy3CH/s1600/%CE%A6%CE%91%CE%99%CE%9D%CE%9F%CE%9C%CE%95%CE%9D%CE%9F+COMPTON(3).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii-zEi30SU3U8JJp6VpVnO1UxvBHatWOuos8iV1C8Idl3ikA_kOl3GF40syvuTsAEUTo7aB-oseVhYoV-TRA8HP7DG-fgMfyBwIYKNY1wyyNEbUcFuxJQ-dJ_lj8_VyPmRpWApN8vdy3CH/s1600/%CE%A6%CE%91%CE%99%CE%9D%CE%9F%CE%9C%CE%95%CE%9D%CE%9F+COMPTON(3).gif" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; line-height: 16px; text-align: start;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Φωτόνιο μήκους κύματος λ έρχεται από αριστερά,σκεδάζεται σε ακίνητο στόχο και ένα νέο φωτόνιο μήκους κύματος λ’ φεύγει με γωνία θ ως προς την ευθεία που ορίζει η αρχική διεύθυνση της προσπίπτουσας δέσμης φωτονίων</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Τα πράγματα φωτίζονται αν δούμε την ηλεκτρομαγνητική ακτινοβολία ως ρεύμα φωτονίων,δηλαδή σωματίων με μηδενική μάζα ηρεμίας που μεταφέρουν ενέργεια και ορμή.Τότε το πρόβλημα της σκέδασης της ακτινοβολίας μετατρέπεται σε πρόβλημα κρούσης ανάμεσα σ' ένα φωτόνιο και ένα ηλεκτρόνιο.</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicUGY6NraLWxo4u0mnKoRwQK5Qah4HexDBmp4KE3gxHZ4C3-pdANf6laGFWwarielgtkg69csKPKR_dom3ROLTAYexqm8MLLU168Nw0kBQ5e1bJYvC85IRKTggYdp6GSx2HWWzhmRlEhk/s1600/%CE%9A%CE%92%CE%91%CE%9D%CE%A4%CE%9F%CE%9C%CE%97%CE%A7%CE%91%CE%9D%CE%99%CE%9A%CE%97(12).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicUGY6NraLWxo4u0mnKoRwQK5Qah4HexDBmp4KE3gxHZ4C3-pdANf6laGFWwarielgtkg69csKPKR_dom3ROLTAYexqm8MLLU168Nw0kBQ5e1bJYvC85IRKTggYdp6GSx2HWWzhmRlEhk/s1600/%CE%9A%CE%92%CE%91%CE%9D%CE%A4%CE%9F%CE%9C%CE%97%CE%A7%CE%91%CE%9D%CE%99%CE%9A%CE%97(12).gif" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">Μετά τη σκέδαση το φωτόνιο κινείται σχηματίζοντας γωνία </span><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">φ </span><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">με την αρχική διεύθυνση κίνησης και έχοντας χάσει τμήμα της αρχικής του ενέργειας αφού ένα μέρος της αρχικής του ενέργειας θα μεταφερθεί στο ηλεκτρόνιο</span></span></b><span style="font-family: "verdana" , sans-serif; line-height: 16px; text-align: justify;"> </span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Ας υποθέσουμε ότι ένα φωτόνιο μήκους κύματος <b>λ</b> συγκρούεται μ' ένα πρακτικώς ακίνητο ηλεκτρόνιο.Μετά τη σκέδαση το φωτόνιο κινείται σχηματίζοντας γωνία <b>φ </b>με την αρχική διεύθυνση κίνησης και έχοντας χάσει τμήμα της αρχικής του ενέργειας αφού ένα μέρος της αρχικής του ενέργειας θα μεταφερθεί στο ηλεκτρόνιο.Το σκεδαζόμενο φωτόνιο θα έχει μετατραπεί σε φωτόνιο μήκους κύματος <b>λ’</b> με<b> λ’>λ.</b>Κατά τη διάρκεια της σκέδασης πρέπει να διατηρούνται η ενέργεια και η ορμή του συστήματος.</span></div>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNtQ47XHcvphF-L6EwuSYm23d8dWzqR1MQRVGQi4a3ejpdkvVuQOnETSK4N7UNGM-SxPvBPEnlwv2G-qNBhglJEXWQlNImkpCnoPNX_Urw4QAkkmDTxfXpCgS-X4IHPqm6DrbS3zEqxKE/s1600/%25CE%25A6%25CE%2591%25CE%2599%25CE%259D%25CE%259F%25CE%259C%25CE%2595%25CE%259D%25CE%259F+COMPTON5.GIF" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNtQ47XHcvphF-L6EwuSYm23d8dWzqR1MQRVGQi4a3ejpdkvVuQOnETSK4N7UNGM-SxPvBPEnlwv2G-qNBhglJEXWQlNImkpCnoPNX_Urw4QAkkmDTxfXpCgS-X4IHPqm6DrbS3zEqxKE/s1600/%25CE%25A6%25CE%2591%25CE%2599%25CE%259D%25CE%259F%25CE%259C%25CE%2595%25CE%259D%25CE%259F+COMPTON5.GIF" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Φαινόμενο Compton</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Το φωτόνιο έχει πριν τη σκέδαση ενέργεια <b>Ε=h</b></span><span style="font-family: "verdana" , sans-serif;"><b>·</b></span><b style="font-family: verdana, sans-serif;">f=h</b><span style="font-family: "verdana" , sans-serif;"><b>·</b></span><b style="font-family: verdana, sans-serif;">c/λ</b><span style="font-family: "verdana" , sans-serif;"> και μετά τη σκέδαση </span><b style="font-family: verdana, sans-serif;">Ε'=h</b><span style="font-family: "verdana" , sans-serif;"><b>·</b></span><b style="font-family: verdana, sans-serif;">c/λ'.</b><br />
<span style="font-family: "verdana" , sans-serif;"> Θα πρέπει λοιπόν να ισχύει</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span><b><span style="color: red;"><span style="font-family: "verdana" , sans-serif;"> </span></span></b><b style="font-family: Verdana, sans-serif;"><span style="color: red;"> </span></b><b><span style="color: red;"><span style="font-family: "verdana" , sans-serif;">hc/λ=</span><span style="font-family: "verdana" , sans-serif;">h</span></span></b><span style="font-family: "verdana" , sans-serif;"><span style="color: red;"><b>·</b></span></span><b><span style="color: red;"><span style="font-family: "verdana" , sans-serif;">c/λ'+</span><span style="font-family: "verdana" , sans-serif;">K<span style="font-size: x-small;">e</span></span></span></b><br />
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<span style="font-family: "verdana" , sans-serif;">όπου: </span><br />
<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">K<span style="font-size: x-small;">e</span></span> η<span style="color: blue;"> κινητική ενέργεια </span>του ανακρουσμένου ηλεκτρονίου.</b></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju4cCTRqqM5wpLv8ikwn3oyO0GF1IHMdwLDsYn-fuFKPSzr4UbRTm7iB0qzYp8LVJ9w4wpBUvH1NQTgieTKApj1TU-cqAcAp5133Nxe6AhZ5iIpUUF8lyp8lxqbdzLAqe8jXI0wTNJ3c07/s1600/%25CE%25A6%25CE%2591%25CE%2599%25CE%259D%25CE%259F%25CE%259C%25CE%2595%25CE%259D%25CE%259F+COMPTON%25284%2529.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju4cCTRqqM5wpLv8ikwn3oyO0GF1IHMdwLDsYn-fuFKPSzr4UbRTm7iB0qzYp8LVJ9w4wpBUvH1NQTgieTKApj1TU-cqAcAp5133Nxe6AhZ5iIpUUF8lyp8lxqbdzLAqe8jXI0wTNJ3c07/s1600/%25CE%25A6%25CE%2591%25CE%2599%25CE%259D%25CE%259F%25CE%259C%25CE%2595%25CE%259D%25CE%259F+COMPTON%25284%2529.gif" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><span style="text-align: start;">H ένταση του σκεδασμένου φωτός συναρτήσει του μήκους κύματος λ' </span><span style="text-align: start;">για τις αναγραφόμενες τιμές της γωνίας σκέδασης.H προσπίπτουσα δέσμη έχει μήκος κύματος λ</span></span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Επειδή το ηλεκτρόνιο μετά την κρούση μπορεί να κινείται με ταχύτητα που πλησιάζει την ταχύτητα του φωτός καλό είναι να χρησιμοποιήσουμε τη σχέση:</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b> </b></span></div>
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<b><span style="font-family: "verdana" , sans-serif;">Κ=m</span></b><span style="font-family: "verdana" , sans-serif;"><b>·</b></span><b><span style="font-family: "verdana" , sans-serif;">c<span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span><span style="background-color: white; font-family: "verdana" , sans-serif;"><span style="line-height: 19px;"><span style="font-size: large;">/</span></span></span></b><b><span style="text-align: -webkit-auto;"><span style="font-family: "arial"; font-size: medium;">(</span><span style="font-family: "verdana" , sans-serif;">1-υ</span></span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span><span style="font-family: "verdana" , sans-serif;">/</span><span style="font-family: "verdana" , sans-serif;">c</span><span style="background-color: white; font-family: "verdana" , sans-serif;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></b><span style="font-family: "trebuchet ms" , sans-serif;"><b>)</b></span><b><span style="background-color: white; font-family: "verdana" , sans-serif;"><sup style="line-height: 19px; text-align: -webkit-auto;">1/2</sup></span></b><b><span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;">-</span><span style="font-family: "verdana" , sans-serif;">m</span><span style="font-family: "verdana" , sans-serif;">·</span><span style="font-family: "verdana" , sans-serif;">c</span><span style="background-color: white; font-family: "verdana" , sans-serif;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span><span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;"> </span></b></div>
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<span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;">για την κινητική ενέργεια οπότε:</span></div>
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<b><span style="font-family: "verdana" , sans-serif;">h</span><span style="font-family: "verdana" , sans-serif;">·</span><span style="font-family: "verdana" , sans-serif;">c/λ=</span><span style="font-family: "verdana" , sans-serif;">h</span></b><span style="font-family: "verdana" , sans-serif;"><b>·</b></span><b><span style="font-family: "verdana" , sans-serif;">c/λ'</span><span style="font-family: "verdana" , sans-serif;">+</span><span style="font-family: "verdana" , sans-serif;">m</span></b><span style="font-family: "verdana" , sans-serif;"><b>·</b></span><b><span style="font-family: "verdana" , sans-serif;">c<span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span><span style="background-color: white; font-family: "verdana" , sans-serif;"><span style="line-height: 19px;"><span style="font-size: large;">/</span></span></span></b><b><span style="text-align: -webkit-auto;"><span style="font-family: "arial"; font-size: medium;">(</span><span style="font-family: "verdana" , sans-serif;">1-υ</span></span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span><span style="font-family: "verdana" , sans-serif;">/</span><span style="font-family: "verdana" , sans-serif;">c</span><span style="background-color: white; font-family: "verdana" , sans-serif;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></b><span style="font-family: "trebuchet ms" , sans-serif;"><b>)</b></span><b><span style="background-color: white; font-family: "verdana" , sans-serif;"><sup style="line-height: 19px; text-align: -webkit-auto;">1/2</sup></span></b><span style="font-family: "verdana" , sans-serif;"><b><span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;">-</span><span style="font-family: "verdana" , sans-serif;">m</span>·</b></span><b><span style="font-family: "verdana" , sans-serif;">c</span><span style="background-color: white; font-family: "verdana" , sans-serif;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span><span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;"> </span></b></div>
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<span style="font-family: "verdana" , sans-serif;"> Η ορμή του φωτονίου πριν είναι <b>p=E/c=h/λ</b> και η ορμή του φωτονίου μετά είναι<b> p'=h/λ'.</b></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjF6vp9DkAL_d2FHrnbEZHs3bKe2c85-XPcPAsaNFPAQ-44bxKlrXuXxXdGsA59XYf5GsxPtKFczvDmUibb3JwLdS9Qy-qz4K5QNctZSZMY7dqd7BRDGaokzwiuew_AqM6e0A_hcRXwJKo/s1600/%CE%9A%CE%92%CE%91%CE%9D%CE%A4%CE%9F%CE%9C%CE%97%CE%A7%CE%91%CE%9D%CE%99%CE%9A%CE%97(15).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjF6vp9DkAL_d2FHrnbEZHs3bKe2c85-XPcPAsaNFPAQ-44bxKlrXuXxXdGsA59XYf5GsxPtKFczvDmUibb3JwLdS9Qy-qz4K5QNctZSZMY7dqd7BRDGaokzwiuew_AqM6e0A_hcRXwJKo/s1600/%CE%9A%CE%92%CE%91%CE%9D%CE%A4%CE%9F%CE%9C%CE%97%CE%A7%CE%91%CE%9D%CE%99%CE%9A%CE%97(15).gif" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple; font-size: small;"><span style="font-family: "verdana" , sans-serif; line-height: 16px; text-align: justify;">Η ορμή του φωτονίου πριν είναι </span><span style="font-family: "verdana" , sans-serif; line-height: 16px; text-align: justify;">p=E/c=h/λ</span><span style="font-family: "verdana" , sans-serif; line-height: 16px; text-align: justify;"> και η ορμή του φωτονίου μετά είναι</span><span style="font-family: "verdana" , sans-serif; line-height: 16px; text-align: justify;"> p'=h/λ'</span></span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Η ορμή του ηλεκτρονίου θα είναι σύμφωνα με τη σχέση: </span></div>
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<b><span style="font-family: "verdana" , sans-serif;">p<span style="font-size: x-small;">e</span>=</span><span style="font-family: "verdana" , sans-serif;">m</span></b><span style="font-family: "verdana" , sans-serif;"><b>·</b></span><b><span style="text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;">υ</span></span><span style="background-color: white; font-family: "verdana" , sans-serif;"><span style="line-height: 19px;"><span style="font-size: large;">/</span></span></span><span style="text-align: -webkit-auto;"><span style="font-family: "arial"; font-size: medium;">(</span><span style="font-family: "verdana" , sans-serif;">1-υ</span></span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span><span style="font-family: "verdana" , sans-serif;">/</span><span style="font-family: "verdana" , sans-serif;">c</span><span style="background-color: white; font-family: "verdana" , sans-serif;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></b><span style="font-family: "trebuchet ms" , sans-serif;"><b>)</b></span><b><span style="background-color: white; font-family: "verdana" , sans-serif;"><sup style="line-height: 19px; text-align: -webkit-auto;">1/2</sup></span></b><br />
<span style="font-family: "trebuchet ms" , sans-serif;"><b><br /></b></span></div>
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<span style="font-family: "verdana" , sans-serif;"> Η διατήρηση της ορμής σε διανυσματική μορφή δίνει:</span></div>
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<span style="font-family: "verdana" , sans-serif;"> </span><br />
<span style="font-family: "verdana" , sans-serif;"><strong>p=p'+p<span style="font-size: x-small;">e </span></strong></span><br />
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<span style="font-family: "verdana" , sans-serif;"></span><span style="font-family: "verdana" , sans-serif;">οπότε:</span><br />
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<strong><span style="font-family: "verdana" , sans-serif;">p<span style="font-size: x-small;">e</span>=p-p'</span></strong><br />
<strong><span style="font-family: "verdana" , sans-serif;"></span></strong><br />
<strong><span style="font-family: "verdana" , sans-serif;"></span></strong></div>
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<span style="font-family: "verdana" , sans-serif;"> Χρησιμοποιώντας τον νόμο του συνημίτονου στο διανυσματικό διάγραμμα του παρακάτω σχήματος προκύπτει:</span></div>
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<span style="font-family: "verdana" , sans-serif;"></span><b><span style="font-family: "verdana" , sans-serif;">p<span style="font-size: x-small;">e</span></span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span><span style="font-family: "verdana" , sans-serif;">=p</span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span><span style="font-family: "verdana" , sans-serif;">+p'</span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span><span style="font-family: "verdana" , sans-serif;">-2pp'συνφ</span></b></div>
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<span style="font-family: "verdana" , sans-serif;"> Δηλαδή:</span><br />
<b><span style="font-family: "verdana" , sans-serif;"><br /></span></b><b><span style="font-family: "verdana" , sans-serif;">m</span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span></b><span style="font-family: "verdana" , sans-serif;"><b>·</b></span><b><span style="text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;">υ</span></span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span><span style="font-family: "verdana" , sans-serif; font-size: x-small; text-align: -webkit-auto;"><span style="line-height: 19px;">/</span></span><span style="text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;">1-υ</span></span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span><span style="font-family: "verdana" , sans-serif;">/</span><span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;"> </span><span style="font-family: "verdana" , sans-serif;">c</span><span style="background-color: white; font-family: "verdana" , sans-serif;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span><span style="font-family: "verdana" , sans-serif; font-size: xx-small; text-align: -webkit-auto;"><span style="line-height: 19px;">=</span></span><span style="font-family: "verdana" , sans-serif;">h<span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span><span style="text-align: -webkit-auto;"><span style="line-height: 19px;">/λ</span></span><span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span></span><span style="text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;">+</span></span><span style="font-family: "verdana" , sans-serif;">h<span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span><span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;"><span style="line-height: 19px;">/λ'</span></span><span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span><span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;">-2</span></span></b><span style="font-family: "verdana" , sans-serif;"><b>·</b></span><b><span style="font-family: "verdana" , sans-serif;">h<span style="background-color: white;"><sup style="line-height: 19px; text-align: -webkit-auto;">2</sup></span><span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;">/</span><span style="text-align: -webkit-auto;"><span style="line-height: 19px;">λ</span></span><span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;"><span style="line-height: 19px;">λ'</span></span></span></b><span style="font-family: "verdana" , sans-serif;"><b>·</b></span><b><span style="font-family: "verdana" , sans-serif;">συνφ</span></b><br />
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<span style="font-family: "verdana" , sans-serif;"> Από τις τελευταίες σχέσεις,αν απαλείψουμε το </span><b style="font-family: verdana, sans-serif;">υ,</b><span style="font-family: "verdana" , sans-serif;">προκύπτει η σχέση:</span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="line-height: 16px; text-align: -webkit-auto;"></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span><b style="font-family: Verdana, sans-serif;"><span style="color: red;"> λ'-λ=h/m</span></b><span style="color: red;"><b><span style="font-family: "verdana" , sans-serif;">·</span><span style="font-family: "verdana" , sans-serif;"><span style="color: red;">c</span></span><span style="font-family: "verdana" , sans-serif;">·</span></b></span><b style="font-family: Verdana, sans-serif;"><span style="color: red;">(1-συνφ)</span></b></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-42661479408157467492016-10-25T18:34:00.000-07:002020-09-12T09:54:54.037-07:00ΘΕΡΜΟΔΥΝΑΜΙΚΗ ΙΣΟΡΡΟΠΙΑ<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="color: red; font-family: Verdana, sans-serif; line-height: 16px; text-align: justify;"><span style="font-size: x-large;">ΘΕΡΜΟΔΥΝΑΜΙΚΗ ΙΣΟΡΡΟΠΙΑ</span></b><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1KoscRNSdtsoSYE33N_RXskwtrCp1XQPkavzwHsVU7VhIEb6iY6D3trmoCOzxgvFb-CfsfzAO9GIwWtY1o5Ru3AUBnvjakgovIQ8ZdUanQ30ERwYXbK7l3e2y8gh888wDv3b7x-8NAR4/s1600/%25CE%2598%25CE%2595%25CE%25A1%25CE%259C%25CE%259F%25CE%2594%25CE%25A5%25CE%259D%25CE%2591%25CE%259C%25CE%2599%25CE%259A%25CE%2597+%25CE%2599%25CE%25A3%25CE%259F%25CE%25A1%25CE%25A1%25CE%259F%25CE%25A0%25CE%2599%25CE%2591.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1KoscRNSdtsoSYE33N_RXskwtrCp1XQPkavzwHsVU7VhIEb6iY6D3trmoCOzxgvFb-CfsfzAO9GIwWtY1o5Ru3AUBnvjakgovIQ8ZdUanQ30ERwYXbK7l3e2y8gh888wDv3b7x-8NAR4/s1600/%25CE%2598%25CE%2595%25CE%25A1%25CE%259C%25CE%259F%25CE%2594%25CE%25A5%25CE%259D%25CE%2591%25CE%259C%25CE%2599%25CE%259A%25CE%2597+%25CE%2599%25CE%25A3%25CE%259F%25CE%25A1%25CE%25A1%25CE%259F%25CE%25A0%25CE%2599%25CE%2591.gif" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-family: Verdana, sans-serif; font-size: large;">ΘΕΡΜΟΔΥΝΑΜΙΚΗ ΙΣΟΡΡΟΠΙΑ</span></b></td></tr>
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<span style="color: red; font-family: "verdana" , sans-serif;"><b>ΕΙΣΑΓΩΓΗ</b></span><br />
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<span style="font-family: "verdana" , sans-serif;"> Ένα θερμοδυναμικό σύστημα π.χ. ένα αέριο μπορεί να να περιγραφεί από τις θερμοδυναμικές μεταβλητές πίεση,όγκο,θερμοκρασία και μάζα.</span><span style="font-family: "verdana" , sans-serif;">Ο <b>όγκος</b>,η <b>πίεση</b> και η <b>θερμοκρασία</b> ορισμένης ποσότητας αερίου σχετίζονται μεταξύ τους με την καταστατική εξίσωση.</span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuzmTJ5vs4G7m38ZoMt8wUNZMoIpN6oJuhqojbq_soFkt9DJQEaykJqma7AGGvfovxXBCV1sx5fws-b5DGQkE5u9JiF1CSaMr8Iom5avaulAPQ6rYHkCLwTxePc6BUuo8OKXazK0ko9kCj/s1600/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(7).jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuzmTJ5vs4G7m38ZoMt8wUNZMoIpN6oJuhqojbq_soFkt9DJQEaykJqma7AGGvfovxXBCV1sx5fws-b5DGQkE5u9JiF1CSaMr8Iom5avaulAPQ6rYHkCLwTxePc6BUuo8OKXazK0ko9kCj/s1600/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(7).jpg" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Ένα θερμοδυναμικό σύστημα π.χ. ένα αέριο μπορεί να να περιγραφεί από τις θερμοδυναμικές μεταβλητές πίεση,όγκο,θερμοκρασία και μάζα</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Για να περιγράψουμε την κατάσταση συγκεκριμένης ποσότητας αερίου αρκούν δύο από αυτά αφού το τρίτο προκύπτει από την καταστατική εξίσωση.</span><strong style="font-family: Verdana, sans-serif;">Οι δύο ποσότητες που είναι ικανές για την περιγραφή της κατάστασης ορισμένης ποσότητας αερίου αποτελούν τις ανεξάρτητες θερμοδυναμικές μεταβλητές του συστήματος</strong><span style="font-family: "verdana" , sans-serif;">.</span><br />
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<span style="color: red; font-family: "verdana" , sans-serif;"><b>ΘΕΡΜΟΔΥΝΑΜΙΚΗ ΙΣΟΡΡΟΠΙΑ</b></span><br />
<span style="font-family: "verdana" , sans-serif;"></span><br /><span style="font-family: "verdana" , sans-serif;"></span>
<b><span style="font-family: "verdana" , sans-serif;"> Όταν σ’ ένα θερμοδυναμικό σύστημα οι θερμοδυναμικές μεταβλητές που το περιγράφουν διατηρούνται σταθερές με το χρόνο,το σύστημα βρίσκεται σε κατάσταση </span><span style="font-family: "verdana" , sans-serif;"><span style="color: blue;">θερμοδυναμικής ισορροπίας</span></span></b><span style="font-family: "verdana" , sans-serif;"><b>.</b>Σε αντίθετη περίπτωση το σύστημα μεταβάλλεται.</span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgABKNoFn5x4amDVsY2d7GHY8-OpL2xPwgdFmKnKsaQVnx2fxT1m4M-XWLSydsNY4zkDavNZLeCT-O0P9cVIi4Sz0RHbmOOwouj1u98BLPmEzXNYslX2jg9arSE7vMpKuvAEjX9eMdPYq0p/s1600/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(3).jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="164" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgABKNoFn5x4amDVsY2d7GHY8-OpL2xPwgdFmKnKsaQVnx2fxT1m4M-XWLSydsNY4zkDavNZLeCT-O0P9cVIi4Sz0RHbmOOwouj1u98BLPmEzXNYslX2jg9arSE7vMpKuvAEjX9eMdPYq0p/s400/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(3).jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b>Όταν η πίεση P,η πυκνότητα ρ και η θερμοκρασία Τ μιας ποσότητας αερίου έχουν η κάθε μια σταθερή τιμή σε όλη την έκταση του όγκου του,τότε λέμε ότι το αέριο βρίσκεται σε </b></span><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b>κατάσταση θερμοδυναμικής ισορροπίας ή απλά ισορροπίας</b></span></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Συνεπώς λέμε:</span><br />
<span style="font-family: "verdana" , sans-serif;"> <b>Όταν η πίεση P,η πυκνότητα ρ και η θερμοκρασία Τ μιας ποσότητας αερίου έχουν η κάθε μια σταθερή τιμή σε όλη την έκταση του όγκου του,τότε λέμε ότι το αέριο βρίσκεται σε </b></span><span style="font-family: "verdana" , sans-serif;"><b>κατάσταση θερμοδυναμικής ισορροπίας ή απλά ισορροπίας.</b></span><br />
<span style="font-family: "verdana" , sans-serif;"><b></b></span><br /><span style="font-family: "verdana" , sans-serif;"><b></b></span>
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj194pkVd8kpPnyyp8LwLxqlk_a4u6iehEYLEtzhJ0scYo3unFwsmGTtCGaOzZfSvVllYO3eJGoH-j61sy0vYcvAnPiAUJrPhlZSZ7MF4FwJRlndv0Hy-Dc_s3NxgtQXMDRJdD2q_WJL8-I/s1600/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(1).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="134" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj194pkVd8kpPnyyp8LwLxqlk_a4u6iehEYLEtzhJ0scYo3unFwsmGTtCGaOzZfSvVllYO3eJGoH-j61sy0vYcvAnPiAUJrPhlZSZ7MF4FwJRlndv0Hy-Dc_s3NxgtQXMDRJdD2q_WJL8-I/s400/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(1).gif" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Όταν ένα θερμό και ένα ψυχρό σώμα έρθουν σε θερμική επαφή,το θερμό σώμα ψύχεται και το ψυχρό θερμαίνεται,μέχρι να αποκτήσουν και τα δύο την ίδια θερμοκρασία</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Όταν ένα θερμό και ένα ψυχρό σώμα έρθουν σε θερμική επαφή,το θερμό σώμα ψύχεται και το ψυχρό θερμαίνεται,μέχρι να αποκτήσουν και τα δύο την ίδια θερμοκρασία.Αυτή η εξισορρόπηση οφείλεται σε ροή θερμότητας από το θερμότερο προς το ψυχρότερο σώμα.Όταν αυτή η ροή θερμότητας έχει σταματήσει,λέμε ότι τα δύο σώματα βρίσκονται σε θερμική ισορροπία.</span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxRnW6gzrgnBv-6ETJTQJ8HxqEoZ-H8r4EaQhtMyAmxjFpoHHTI898Txpq0Mj35BtTQBq_KfdLME1fxVfaxV1G84LupBjfwCsFTWTXTSibXu708n7wCWv8ZW3OsKUEJKNrjOoemfruO7JR/s1600/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(4).jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxRnW6gzrgnBv-6ETJTQJ8HxqEoZ-H8r4EaQhtMyAmxjFpoHHTI898Txpq0Mj35BtTQBq_KfdLME1fxVfaxV1G84LupBjfwCsFTWTXTSibXu708n7wCWv8ZW3OsKUEJKNrjOoemfruO7JR/s1600/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(4).jpg" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="font-family: Verdana, sans-serif; line-height: 16px; text-align: justify;"><span style="color: purple; font-size: small;">Όταν η θερμοκρασία ενός θερμοδυναμικού συστήματος έχει την ίδια σταθερή τιμή σ' όλη την έκταση του,τότε λέμε ότι βρίσκεται σε κατάσταση θερμικής ισορροπίας</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"><b> Όταν η θερμοκρασία ενός θερμοδυναμικού συστήματος έχει την ίδια σταθερή τιμή σ' όλη την έκταση του,τότε λέμε ότι βρίσκεται σε κατάσταση <span style="color: blue;">θερμικής ισορροπίας.</span></b></span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaPO93gCDhnCO7fioMHiyJwuallp5MqUiF8QhvNSEVszC1krZ5SujUg2zXCZqX5JZIO7NeSivFqNEEiDyTjB20-sLShHlW8pyaKumFoR60L_phI5VUckc6qXrMgcVZ7_wa_CCX7DvL7Ep7/s1600/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(2).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaPO93gCDhnCO7fioMHiyJwuallp5MqUiF8QhvNSEVszC1krZ5SujUg2zXCZqX5JZIO7NeSivFqNEEiDyTjB20-sLShHlW8pyaKumFoR60L_phI5VUckc6qXrMgcVZ7_wa_CCX7DvL7Ep7/s1600/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(2).gif" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple; font-family: Verdana, sans-serif; font-size: small;">Ισορροπία θερμοδυναμικού συστήματος</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> <b>Όταν όλες οι θερμοδυναμικές μεταβλητές που περιγράφουν την κατάσταση ενός θερμοδυναμικού συστήματος έχουν η καθεμιά σταθερή τιμή σ' όλη την έκταση του,τότε λέμε ότι το σύστημα βρίσκεται σε κατάσταση <span style="color: blue;">θερμικής ισορροπίας</span> ή απλά <span style="color: blue;">ισορροπίας</span>.</b></span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXsnPIZO78iITq2qPYv_kqfWA8AY7ypRH0vIHBMR0_ToNHrYSpt5M_IObMkv5gip5W2xgx_u8uLiTb7Ky9RpDwL4rxGrhrFkzwZU_fpD-4gmpe_GhS_QvnZn9edpVUUQHpT5-3Dziqnz_a/s1600/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(5).jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="253" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXsnPIZO78iITq2qPYv_kqfWA8AY7ypRH0vIHBMR0_ToNHrYSpt5M_IObMkv5gip5W2xgx_u8uLiTb7Ky9RpDwL4rxGrhrFkzwZU_fpD-4gmpe_GhS_QvnZn9edpVUUQHpT5-3Dziqnz_a/s320/%CE%98%CE%95%CE%A1%CE%9C%CE%9F%CE%94%CE%A5%CE%9D%CE%91%CE%9C%CE%99%CE%9A%CE%97+%CE%99%CE%A3%CE%9F%CE%A1%CE%A1%CE%9F%CE%A0%CE%99%CE%91(5).jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Η κατάσταση ισορροπίας ενός συστήματος είναι μια ιδιαίτερα απλή κατάσταση</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Η κατάσταση ισορροπίας ενός συστήματος είναι μια ιδιαίτερα απλή κατάσταση,γιατί στην κατάσταση αυτή οι θερμοδυναμικές μεταβλητές του συστήματος έχουν η καθεμιά σταθερή τιμή,ανεξάρτητη του χρόνου,και είναι δυνατό να μετρηθούν.</span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMfVMqZyVUsYWZUl_SjKLGXp7fETUqzYhGf9wxlFNxLT38zT4PuDUXa5z0_jA8qNnqoB4ArHb1sPcUqEHHY5Pt4cAipJWZtpUqNmMFOQWgHbH6073r3GHey9q_myUoc_eX2R3EATuJNUn4/s1600/%25CE%2598%25CE%2595%25CE%25A1%25CE%259C%25CE%259F%25CE%2594%25CE%25A5%25CE%259D%25CE%2591%25CE%259C%25CE%2599%25CE%259A%25CE%2597+%25CE%2599%25CE%25A3%25CE%259F%25CE%25A1%25CE%25A1%25CE%259F%25CE%25A0%25CE%2599%25CE%2591%25286%2529.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMfVMqZyVUsYWZUl_SjKLGXp7fETUqzYhGf9wxlFNxLT38zT4PuDUXa5z0_jA8qNnqoB4ArHb1sPcUqEHHY5Pt4cAipJWZtpUqNmMFOQWgHbH6073r3GHey9q_myUoc_eX2R3EATuJNUn4/s1600/%25CE%2598%25CE%2595%25CE%25A1%25CE%259C%25CE%259F%25CE%2594%25CE%25A5%25CE%259D%25CE%2591%25CE%259C%25CE%2599%25CE%259A%25CE%2597+%25CE%2599%25CE%25A3%25CE%259F%25CE%25A1%25CE%25A1%25CE%259F%25CE%25A0%25CE%2599%25CE%2591%25286%2529.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px;"><b><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"> </span><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">Η κατάσταση θερμοδυναμικής ισορροπίας ενός αερίου μπορεί να παρασταθεί γραφικά με ένα σημείο σε σύστημα συντεταγμένων με άξονες δύο ανεξάρτητες θερμοδυναμικές μεταβλητές του συστήματος</span></span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> </span><span style="font-family: "verdana" , sans-serif;">Η κατάσταση θερμοδυναμικής ισορροπίας ενός αερίου μπορεί να παρασταθεί γραφικά με ένα σημείο σε σύστημα συντεταγμένων με άξονες δύο ανεξάρτητες θερμοδυναμικές μεταβλητές του συστήματος.Αν το σύστημα δε βρίσκεται σε ισορροπία η κατάστασή του δε μπορεί να αποδοθεί γραφικά αφού δε μπορούμε να μιλήσουμε για πίεση ή θερμοκρασία του συστήματος.Η πίεση και η θερμοκρασία έχουν διαφορετικές τιμές στα διάφορα σημεία του αερίου.</span><br />
<span style="font-family: "verdana" , sans-serif;"> Άρα:</span><br />
<span style="font-family: "verdana" , sans-serif;"> <b>Η κατάσταση θερμοδυναμικής ισορροπίας ενός αερίου μπορεί να παρασταθεί γραφικά με ένα σημείο.</b></span><span style="font-family: "verdana" , sans-serif; font-weight: bold;">Αν το σύστημα δε βρίσκεται σε ισορροπία η κατάστασή του δε μπορεί να αποδοθεί γραφικά.</span></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-91856853448362567872016-10-24T17:41:00.001-07:002020-09-12T09:54:54.233-07:00ΜΕΤΕΩΡΙΤΗΣ<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="color: red; font-family: "lucida grande", tahoma, verdana, arial, sans-serif;"><span style="font-size: x-large;">ΜΕΤΕΩΡΙΤΗΣ</span></b><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFmLjGfB5sMegT03xjF8M1kgSXyIa8kR4EYw6OGJRw1PHk_LqwOh8eUWOu-wEYzWSyLlWTulD6pg0EolJPlMSG_f6hjYZlwFXp_T0REEQBbI3RuJ9-zdNHtHoLNT7JNYG9Cb0Z_7adIYc/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(1).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFmLjGfB5sMegT03xjF8M1kgSXyIa8kR4EYw6OGJRw1PHk_LqwOh8eUWOu-wEYzWSyLlWTulD6pg0EolJPlMSG_f6hjYZlwFXp_T0REEQBbI3RuJ9-zdNHtHoLNT7JNYG9Cb0Z_7adIYc/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(1).gif" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: large;"><b>ΜΕΤΕΩΡΙΤΗΣ</b></span></td></tr>
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<strong style="font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; line-height: 16px;"><span style="color: red;">ΕΙΣΑΓΩΓΗ</span></strong></div>
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<span style="font-family: "verdana" , sans-serif;"><strong> <span style="color: blue;">Μετέωρο</span></strong><b> ονομάζεται το μικρό ουράνιο σώμα <span style="text-align: -webkit-auto;">συνήθως του μεγέθους μικρών κόκκων άμμου και χαλίκων </span>το οποίο όταν πλησιάζει τη Γη,έλκεται από αυτήν και κινείται προς την επιφάνειά της με ολοένα και μεγαλύτερη ταχύτητα.</b></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO0LoHp7X8aJQM9v3ro7MtwSryLHBc3zWtnldhyTEHWQR7k9_8MEIL8naPD-sATMtaJMEixwGE-8wGClCHXeNwlsZXplxRQqod4_cmaamYCpc4X3w7slnfi_tan86M811zG4wm332yHqc/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(4).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO0LoHp7X8aJQM9v3ro7MtwSryLHBc3zWtnldhyTEHWQR7k9_8MEIL8naPD-sATMtaJMEixwGE-8wGClCHXeNwlsZXplxRQqod4_cmaamYCpc4X3w7slnfi_tan86M811zG4wm332yHqc/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(4).gif" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="color: purple; font-size: small;"><strong style="font-family: Verdana, sans-serif; line-height: 16px; text-align: justify;">Μετέωρο</strong><b style="font-family: Verdana, sans-serif; line-height: 16px; text-align: justify;"> ονομάζεται το μικρό ουράνιο σώμα <span style="text-align: -webkit-auto;">συνήθως του μεγέθους μικρών κόκκων άμμου και χαλίκων </span>το οποίο όταν πλησιάζει τη Γη,έλκεται από αυτήν και κινείται προς την επιφάνειά της με ολοένα και μεγαλύτερη ταχύτητα</b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Το μετέωρο β</span><span style="text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;">ρίσκεται διάσπαρτο σε όλο το χώρο του ηλιακού συστήματος.</span></span><span style="font-family: "verdana" , sans-serif;">Το μετέωρο </span><span style="font-family: "verdana" , sans-serif;">όταν πλησιάζει τη <b>Γη</b> </span><span style="font-family: "verdana" , sans-serif;">ιονίζει τα μόρια του αέρα και την φωτεινή ακτινοβολία.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="text-align: -webkit-auto;"><b> Το σύνολο των μετεώρων αποτελεί την καλούμενη <span style="color: blue;">μετεωρική ύλη</span>.</b></span></span><br />
<b><span style="font-family: "verdana" , sans-serif;"> Όταν το μετέωρο εισέλθει στην ατμόσφαιρα της</span><span style="font-family: "verdana" , sans-serif;"> Γης</span><span style="font-family: "verdana" , sans-serif;"> και ανεξάρτητα του πότε γίνεται αντιληπτό χαρακτηρίζεται </span><span style="font-family: "verdana" , sans-serif;"><span style="color: blue;">μετεωρίτης</span></span><span style="font-family: "verdana" , sans-serif;">.</span></b></div>
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<span style="color: red; font-family: "verdana" , sans-serif;"><b>ΕΙΔΗ ΜΕΤΕΩΡΩΝ</b></span><br />
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<span style="font-family: "verdana" , sans-serif;"> Τα μετέωρα ανάλογα με την μάζα τους και την λαμπρότητά τους διακρίνονται:</span></div>
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<b><span style="font-family: "verdana" , sans-serif;"><span style="color: red;">α)</span> </span><span style="font-family: "verdana" , sans-serif;"><span style="color: blue;">Διάττοντες</span></span></b><span style="font-family: "verdana" , sans-serif;"><b><span style="color: blue;">:</span></b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b> Τα μετέωρα αυτά έχουν πολύ μικρή μάζα (περίπου όσο ένας κόκκος άμμου) και λαμπρότητα.</b></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz5j2Qz8Qm91aHQRZU70JitkoITk-dBkf80qI5Fkki0CTJap3E88gl6eu5wFoPEInqMGnG0e1Lp9NI-5N24l33G1rKZxsIChefCLA15ZuIiwfWIW5mcSRkwfK_M54BcJriykSc4ggYhPw/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(6).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz5j2Qz8Qm91aHQRZU70JitkoITk-dBkf80qI5Fkki0CTJap3E88gl6eu5wFoPEInqMGnG0e1Lp9NI-5N24l33G1rKZxsIChefCLA15ZuIiwfWIW5mcSRkwfK_M54BcJriykSc4ggYhPw/s400/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(6).gif" width="400" /></a></td></tr>
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<span style="color: purple; font-size: small;"><b><span style="font-family: "verdana" , sans-serif;">Διάττοντες </span></b><b style="font-family: Verdana, sans-serif;">έχουν πολύ μικρή μάζα και λαμπρότητα</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"> Παρατηρούνται συχνότερα από όλα τα μετέωρα.</span></div>
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<b><span style="font-family: "verdana" , sans-serif;"><span style="color: red;">β)</span> </span><span style="font-family: "verdana" , sans-serif;"><span style="color: blue;">Βολίδες</span></span><span style="font-family: "verdana" , sans-serif;"><span style="color: blue;">:</span></span></b></div>
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<span style="font-family: "verdana" , sans-serif;"><b> Τα μετέωρα αυτά είναι πιο λαμπρά και πιο εντυπωσιακά φαινόμενα και δίνουν πολλές φορές και σκιά.</b></span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7vCbngeVWdM4Cw00puw19FsnQExXe5I94o3ULVbE-Rr_3efySbZ7MLdfZOMft_-cuOH4WfNTu5zeJFhOCQr51QEnIWihdB71qFa26cU2zLFvtG5qQf_hlJ5djDJbHj6ds-D0ax_u-83k/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(7).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7vCbngeVWdM4Cw00puw19FsnQExXe5I94o3ULVbE-Rr_3efySbZ7MLdfZOMft_-cuOH4WfNTu5zeJFhOCQr51QEnIWihdB71qFa26cU2zLFvtG5qQf_hlJ5djDJbHj6ds-D0ax_u-83k/s320/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(7).gif" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">Οι βολίδες είναι πιο λαμπρά και πιο εντυπωσιακά φαινόμενα </span> </span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Επίσης δ</span><span style="font-family: "verdana" , sans-serif;">ιαρκούν περισσότερο και τις περισσότερες φορές συνοδεύονται από έκρηξη.</span><span style="font-family: "verdana" , sans-serif;">Παρατηρούνται πολύ </span><span style="font-family: "verdana" , sans-serif;">σπάνια.</span></div>
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<b><span style="font-family: "verdana" , sans-serif;"><span style="color: red;">γ)</span> </span><span style="font-family: "verdana" , sans-serif;"><span style="color: blue;">Μετεωρίτες</span></span><span style="font-family: "verdana" , sans-serif;"><span style="color: blue;">:</span> </span></b></div>
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<b><span style="font-family: "verdana" , sans-serif;"><span style="font-family: "verdana" , sans-serif;"> Οι μετεωρίτες έχουν αρκετά μεγάλη μάζα ώστε να μην εξαερωθούν τελείως,κατά τη διαδρομή του</span><span style="font-family: "verdana" , sans-serif;">ς στην ατμόσφαιρα,και μερικά μέρη τους να φτάσουν στην επιφάνεια.</span></span></b><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvbWhGKk0LXJ0_Vf8ea__j_fG5bU1x29jN3xcvE9Djs31us0tMIhMp5seoLR46eBLppWxYxds5z2NWMr5nQpiaWk0ewxUbexrTLy4xKljjPzbTbyhB8HqQdSqEckmQVoOJTW4THNDlPUw/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(8).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="261" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvbWhGKk0LXJ0_Vf8ea__j_fG5bU1x29jN3xcvE9Djs31us0tMIhMp5seoLR46eBLppWxYxds5z2NWMr5nQpiaWk0ewxUbexrTLy4xKljjPzbTbyhB8HqQdSqEckmQVoOJTW4THNDlPUw/s400/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(8).gif" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="line-height: 16px; text-align: justify;"><span style="font-family: "verdana" , sans-serif;"><span style="color: purple; font-size: small;">Οι μετεωρίτες έχουν αρκετά μεγάλη μάζα ώστε να μην εξαερωθούν τελείως</span></span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Όταν οι μετεωρίτες εισέρχονται στη γήινη ατμόσφαιρα,οι ταχύτητές τους κυμαίνονται από <b>36.000</b> έως και <b>250.000 χιλιόμετρα την ώρα</b>.Στη συνέχεια επιβραδύνονται και η ταχύτητά τους μειώνεται σε μερικές εκατοντάδες χιλιόμετρα την ώρα,για να καταλήξουν στην επιφάνεια της <b>Γης</b> με ένα χαρακτηριστικό σάλπισμα.</span><br />
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<span style="font-family: "verdana" , sans-serif;"><span style="color: red;"><b>ΧΑΡΑΚΤΗΡΙΣΤΙΚΑ </b></span><b style="color: red;">ΤΩΝ ΜΕΤΕΩΡΩΝ</b></span><br />
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<span style="font-family: "verdana" , sans-serif;"> Η φωτοβολία των μετεώρων αρχίζει σε ύψος <b>100-120 km</b> περίπου και σταματάει σε <b>20-90 km </b>ανάλογα με το μέγεθος του μετεώρου.Το φάσμα τους περιέχει τις χαρακτηριστικές ταινίες ιονισμένων μορίων του αέρα καθώς και συνηθισμένων στοιχείων<b>(H,N,Mg,Ca και Fe).</b></span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsTJ1-QB9GW8UkcmTi6l_ZxtqFUPvYar_VvNrZTGS32TXPoEQSksKNhbr-mJT8JDqeMgrYAyhzxB2LcreedKEGRkOEpgzw8W_tkjebT1wVWJwIjQTtKKQU3wNoc-MrFbeinLE0BbD2cS0/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(3).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsTJ1-QB9GW8UkcmTi6l_ZxtqFUPvYar_VvNrZTGS32TXPoEQSksKNhbr-mJT8JDqeMgrYAyhzxB2LcreedKEGRkOEpgzw8W_tkjebT1wVWJwIjQTtKKQU3wNoc-MrFbeinLE0BbD2cS0/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(3).gif" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Η φωτοβολία των μετεώρων αρχίζει σε ύψος 100-120 km περίπου και σταματάει σε 20-90 km ανάλογα με το μέγεθος του μετεώρου</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> </span><span style="text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;">Τα μετέωρα,που προέρχονται κυρίως από τη διάλυση κομητών, κινούνται με μεγάλες ταχύτητες που φθάνουν τα <b>15</b> έως <b>45 km/s</b>,όση δηλαδή και η ταχύτητα των κομητών,η δε κίνησή τους γίνεται επί ελλειπτικών,παραβολικών και υπερβολικών τροχιών.</span></span><span style="text-align: -webkit-auto;"><span style="font-family: "verdana" , sans-serif;">Σημειώνεται ότι ταχύτητα μέχρι <b>42 km/s </b>αντιστοιχεί σε ελλειπτική τροχιά,που είναι μεν ίση με <b>42 km/s</b> στη παραβολική,ενώ μεγαλύτερη στη υπερβολική.</span></span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1kdmgfieoYbqLd2TrRlsKWnODINcgGP84HbKqzOsQ19wzBXo61Cu3ghtSxXcJB07WTqnoRsIrcIYyenzFuW95owobPdA3ujABQind2mHbNXpeuNToYS0jz4ECLNnrT61rC4odUQS-_wI/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(2).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="194" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1kdmgfieoYbqLd2TrRlsKWnODINcgGP84HbKqzOsQ19wzBXo61Cu3ghtSxXcJB07WTqnoRsIrcIYyenzFuW95owobPdA3ujABQind2mHbNXpeuNToYS0jz4ECLNnrT61rC4odUQS-_wI/s200/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(2).gif" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Τα μετέωρα κινούνται με μεγάλες ταχύτητες που φθάνουν τα 15 έως 45 km/s</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"><span style="text-align: -webkit-auto;"> Όταν η <b>Γη</b>,που κινείται γύρω από τον <b>Ήλιο </b>με ταχύτητα <b>30 km/s </b>περίπου,συναντήσει μετέωρο τότε,από τη σύνθεση της ταχύτητας <b>Γης-μετεώρου</b>,αυτό υφίσταται τόση τριβή με τα μόρια της </span><span style="background-color: white; line-height: 18.2px; text-align: left;">γήινης</span><span style="background-color: white; line-height: 18.2px; text-align: left;"> </span><span style="text-align: -webkit-auto;"> ατμόσφαιρας ώστε στο ύψος των <b>120 km,</b>λόγω της αναπτυσσόμενης θερμότητας να διαπυρώνεται εξωτερικά.Αν αυτό είναι μικρών διαστάσεων,δηλαδή του μεγέθους του κόκκου άμμου,τότε κατακαίεται και αποτεφρώνεται μέσα στην ατμόσφαιρα σε διάστημα <b>2-3 δευτερολέπτων.</b></span></span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOPBAhoYtzTBzFR9CgQI32d2ClLNBMZ2Fd2tq3kAaeiSFXo9xgB5e3ldB4_Uy545-nsz-hbUwVWqm68kcKamE_vrCtpp9GpLTMAHn6N0iSeiKHsv8uwNN5SJ3z0eJ-znCk-dY0KCD9zUU/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(5).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOPBAhoYtzTBzFR9CgQI32d2ClLNBMZ2Fd2tq3kAaeiSFXo9xgB5e3ldB4_Uy545-nsz-hbUwVWqm68kcKamE_vrCtpp9GpLTMAHn6N0iSeiKHsv8uwNN5SJ3z0eJ-znCk-dY0KCD9zUU/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(5).gif" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Οι λαμπρότεροι διάττοντες και οι βολίδες συνοδεύονται από μια φωτεινή ουρά η οποία διατηρείται μερικά λεπτά μετά την εξαέρωση του μετεώρου</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Οι λαμπρότεροι διάττοντες και οι βολίδες συνοδεύονται από μια φωτεινή ουρά η οποία διατηρείται μερικά λεπτά μετά την εξαέρωση του μετεώρου.Οι ουρές αυτές δεν είναι πάντα ευθύγραμμες και συχνά παρουσιάζουν κυματισμούς ή και καμπές.</span></div>
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<span style="font-family: "verdana" , sans-serif;"> Αρκετά εκατομμύρια μετεώρων πέφτουν σε όλη τη <b>Γη</b> κάθε εικοσιτετράωρο.Ο αριθμός αυτός δεν είναι σταθερός αλλά σε μερικές περιόδους το φαινόμενο παρουσιάζεται αρκετά έντονο,οπότε λέμε ότι έχουμε βροχή διαττόντων.Δεν είναι δυνατός ο υπολογισμός της μάζας που προσθέτουν στον πλανήτη μας αλλά γενικά θεωρείται ελάχιστη.</span></div>
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<span style="color: red; font-family: "verdana" , sans-serif;"><b>ΠΑΡΑΤΗΡΗΣΗ </b></span><b style="font-family: Verdana, sans-serif;"><span style="color: red;">ΤΩΝ ΜΕΤΕΩΡΩΝ</span></b></div>
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<span style="font-family: "verdana" , sans-serif;"> Οι παρατηρήσεις των μετεώρων γίνονται με ειδικές φωτογραφικές μηχανές καθώς και με ραντάρ,καθόσον τα ιονισμένα ίχνη τους ανακλούν τα μικροκύματα.Αυτό σημαίνει ότι είναι δυνατόν να γίνουν παρατηρήσεις ακόμα και την ημέρα.Ο υπολογισμός του ύψους της τροχιάς τους γίνεται εύκολα με τριγωνομετρικές μεθόδους,αφού γίνουν ταυτόχρονες παρατηρήσεις από δύο σταθμούς που απέχουν μεταξύ τους μερικές δεκάδες χιλιόμετρα.</span></div>
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<span style="font-family: "verdana" , sans-serif;"> Τα αποτελέσματα των παρατηρήσεων δείχνουν εξάλλου ότι υπάρχουν δύο τύποι μετεώρων:</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">α) </span><span style="color: blue;">Τα σποραδικά μετέωρα.</span></b></span><br />
<b style="font-family: Verdana, sans-serif;"></b><b style="font-family: Verdana, sans-serif;"> Τα σποραδικά μετέωρα </b><b style="font-family: Verdana, sans-serif;">ε</b><b style="font-family: Verdana, sans-serif;">μφανίζονται τυχαία και έρχονται από τυχαία διεύθυνση και</b></div>
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="font-size: small;"><span style="color: purple;"><b style="font-family: verdana, sans-serif; line-height: 16px; text-align: justify;">Τα σποραδικά μετέωρα </b></span><b style="font-family: verdana, sans-serif; line-height: 16px; text-align: justify;"><span style="color: purple;">ε</span></b><span style="color: purple;"><b style="font-family: verdana, sans-serif; line-height: 16px; text-align: justify;">μφανίζονται τυχαία και έρχονται από τυχαία διεύθυνση </b></span></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;"> </span></b></span><span style="font-family: "verdana" , sans-serif;">Ο αριθμός των ορατών <b>σποραδικών μετεώρων </b>ποικίλλει κατά τη διάρκεια της νύχτας,από <b>4-6 </b>ανά ώρα περίπου.</span><br />
<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">β)</span> <span style="color: blue;">Οι βροχές μετεώρων</span> ή <span style="color: blue;">βροχές διαττόντων</span>,όπως είναι πιο γνωστές,κατά τις οποίες τα μετέωρα έρχονται από την ίδια διεύθυνση ξεκινώντας προφανώς από την ίδια περιοχή(ακτινοβόλο σημείο) και προέρχονται από ένα μετεωρικό ρεύμα που σχηματίσθηκε από την αποσύνθεση κομήτη και περιφέρεται γύρω από τον Ήλιο</b>.</span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlIalzHGh4qmdZLU6Bnam_LZfMkZs2Quy4895AspXHSF0gBfkhG8t6viyjfDF322PcMJpgANKJc5CMj7tUu1GVvR82O79VPvvuemSIfJDNuhpiDvjyl6Y3aBUe27vihVCKACTXX92SEXY/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(11).gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlIalzHGh4qmdZLU6Bnam_LZfMkZs2Quy4895AspXHSF0gBfkhG8t6viyjfDF322PcMJpgANKJc5CMj7tUu1GVvR82O79VPvvuemSIfJDNuhpiDvjyl6Y3aBUe27vihVCKACTXX92SEXY/s1600/%CE%9C%CE%95%CE%A4%CE%95%CE%A9%CE%A1%CE%9F(11).gif" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="color: purple; font-size: small;"><b style="font-family: verdana, sans-serif; line-height: 16px; text-align: justify;">Οι βροχές μετεώρων</b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Οι βροχές μετεώρων χαρακτηρίζονται με το όνομα του αστερισμού στον οποίο βρίσκεται το ακτινοβόλο σημείο τους.</span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;"><b><span style="color: purple;">Οι βροχές μετεώρων Λεωνίδες</span></b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Έτσι λέμε π.χ.<b> Περσίδες,Ωριωνίδες,Λεωνίδες κ.λπ.</b></span></div>
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<strong><span style="color: red; font-family: "verdana" , sans-serif; font-size: large;"><br /></span></strong><strong><span style="color: red; font-family: "verdana" , sans-serif;">ΟΡΙΣΜΟΙ ΤΩΝ ΜΕΤΕΩΡΩΝ</span></strong></div>
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<span style="font-family: "verdana" , sans-serif;"> Η ονοματολογία που χρησιμοποιούμε για τα μικρά αυτά αντικείμενα εξαρτάται από την ακριβή θέση τους στο <b>Διάστημα</b>.Τα διάφορα μικρά τεμάχια, με διάμετρο σωματιδίου σκόνης και μέχρι μερικά μέτρα,που περιφέρονται στον διαπλανητικό χώρο,ονομάζονται <strong>μετεωροειδή</strong>.</span><br />
<span style="font-family: "verdana" , sans-serif;"> Όταν αυτά τα αντικείμενα εισέρχονται στην ατμόσφαιρα της <b>Γης,</b>σχηματίζουν,λόγω της τριβής τους,μια λαμπερή ουρά.Όσα από αυτά εξαερώνονται,ονομάζονται <strong>μετέωρα</strong>,ενώ τα μεγαλύτερα απ' αυτά,που καταφέρνουν να φτάσουν μέχρι την επιφάνεια της <b>Γης</b>,σχηματίζοντας μικρούς ή μεγάλους κρατήρες,ονομάζονται<b> μετεωρίτες.</b></span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><b><span style="color: purple;"><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">Τα διάφορα μικρά τεμάχια,με διάμετρο σωματιδίου σκόνης και μέχρι μερικά μέτρα,που περιφέρονται στον διαπλανητικό χώρο,ονομάζονται </span><span style="font-family: "verdana" , sans-serif; font-size: small; line-height: 16px; text-align: justify;">μετεωροειδή</span></span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Όταν το μετέωρο εισέλθει στην ατμόσφαιρα της<b> Γης</b> και ανεξάρτητα του πότε γίνεται αντιληπτό χαρακτηρίζεται <b>μετεωρίτης</b>.</span></div>
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<span style="font-family: "verdana" , sans-serif;"> Όταν ο μετεωρίτης παρατηρείται ως αστέρας που κινείται ταχύτατα αφήνοντας πίσω του φωτεινή ουρά λέγεται "διάττων αστήρ" ή <b>Διάττοντας αστέρας.</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"> Όταν όμως το μετέωρο ή μετεωρίτης έχει μεγαλύτερες διαστάσεις,όπου τότε πυρακτώνεται και εκρήγνυται με συνοδεία κρότου,ονομάζεται <b>βολίδα</b> ή <b>"φαινόμενο βολίδας"</b>.</span></div>
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<span style="font-family: "verdana" , sans-serif;"> Όταν το μετέωρο είναι μεγαλύτερο από το μέγεθος ενός καρυδιού,τότε δεν προλαβαίνει ν΄ αποτεφρωθεί μέσα στην ατμόσφαιρα και πέφτει καιγόμενο στο έδαφος.Επειδή τότε έχει πάψει πλέον να "μετεωρεί" ονομάζεται μετεωρόλιθος ή αερόλιθος.Συμβαίνει όμως πολλές φορές να χρησιμοποιείται εσφαλμένα ο όρος μετεωρίτης για τους αερόλιθους.</span></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-15826029356028163242016-10-23T17:19:00.003-07:002020-09-12T09:54:54.432-07:00ΕΝΕΡΓΕΙΑ ΔΙΕΓΕΡΣΗΣ<div dir="ltr" style="text-align: left;" trbidi="on">
<b style="font-family: verdana, sans-serif; text-align: justify;"><span style="color: red; font-size: x-large;">ΕΝΕΡΓΕΙΑ ΔΙΕΓΕΡΣΗΣ</span></b><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: large;"><b>ΕΝΕΡΓΕΙΑ ΔΙΕΓΕΡΣΗΣ</b></span></td></tr>
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<span style="font-family: "verdana" , sans-serif;"><span style="color: red; font-family: "verdana" , sans-serif; text-align: -webkit-auto;"><b>ΕΙΣΑΓΩΓΗ</b></span></span><br />
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<span style="font-family: "verdana" , sans-serif;"> Αν το άτομο του υδρογόνου που βρίσκεται στη θεμελιώδη κατάσταση απορροφήσει ενέργεια,τότε το ηλεκτρόνιο μπορεί να μεταπηδήσει σε άλλη επιτρεπόμενη τροχιά υψηλότερης ενέργειας.</span><br />
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<span style="font-family: "verdana" , sans-serif;"><span style="color: red; font-family: "verdana" , sans-serif; text-align: -webkit-auto;"><b>ΔΙΕΓΕΡΣΗ ΤΟΥ ΑΤΟΜΟΥ</b></span></span><br />
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<span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;"><b> Η μετάβαση ενός ηλεκτρονίου του ατόμου από μία τροχιά χαμηλής ενέργειας σε άλλη υψηλότερης ενέργειας ονομάζεται <span style="color: blue;">διέγερση του ατόμου</span>.</b></span><br />
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<tr><td class="tr-caption" style="font-size: 13px;"><b style="text-align: justify;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;">Η μετάβαση ενός ηλεκτρονίου του ατόμου από μία τροχιά χαμηλής ενέργειας σε άλλη υψηλότερης ενέργειας ονομάζεται διέγερση του ατόμου</span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"> Το διεγερμένο άτομο παραμένει στην κατάσταση διέγερσης για ελάχιστο χρονικό διάστημα (της τάξης του </span><b style="font-family: verdana, sans-serif;"><span style="background-color: white; text-indent: 10px;">10</span><sup class="small_font" style="background-color: white; text-indent: 10px;">-8 </sup></b><span style="background-color: white; font-family: "verdana" , sans-serif; text-indent: 10px;"><b>s</b>)</span><span style="font-family: "verdana" , sans-serif;"> και επανέρχεται στη θεμελιώδη κατάσταση.</span><br />
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">ΕΝΕΡΓΕΙΑ ΔΙΕΓΕΡΣΗΣ</span></b></span><br />
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<span style="font-family: "verdana" , sans-serif; text-align: -webkit-auto;"><b> Η ενέργεια που απαιτείται για τη διέγερση του ατόμου ονομάζεται <span style="color: blue;">ενέργεια διέγερσης</span>.</b></span><br />
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<tr><td class="tr-caption" style="font-size: 12.8px;"><b style="font-family: verdana, sans-serif; text-align: justify;"><span style="color: purple; font-size: small;">Η ενέργεια που απαιτείται για τη διέγερση του ατόμου ονομάζεται <span style="color: blue;">ενέργεια διέγερσης</span></span></b></td></tr>
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<span style="font-family: "verdana" , sans-serif;"><b> </b>Η επάνοδος του ηλεκτρονίου στη θεμελιώδη κατάσταση μπορεί να γίνει είτε απευθείας με ένα άλμα,οπότε εκπέμπεται ένα φωτόνιο,είτε με περισσότερα διαδοχικά άλματα,οπότε εκπέμπονται τόσα φωτόνια όσα και τα άλματα που πραγματοποιεί.</span></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.comtag:blogger.com,1999:blog-6644102595821010388.post-85126525681576533012016-10-13T19:08:00.000-07:002020-09-12T09:54:54.626-07:00ΤΥΠΟΙ ΟΜΙΧΛΗΣ <div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="color: red; font-family: "verdana" , sans-serif; font-size: x-large;"><b>ΤΥΠΟΙ ΟΜΙΧΛΗΣ </b></span></div>
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<tr><td class="tr-caption" style="text-align: center;"><b><span style="color: purple; font-family: "verdana" , sans-serif; font-size: large;">ΤΥΠΟΙ ΟΜΙΧΛΗΣ </span></b></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">ΕΙΣΑΓΩΓΗ</span></b></span><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span style="color: red;"> </span><span style="color: blue;">Ομίχλη</span></b><b> ονομάζεται το νέφος που επικάθεται στην επιφάνεια της Γης και προκαλεί ελάττωση της οριζόντιας ορατότητας σε αποστάσεις μικρότερες των 1.000 μ.</b></span><br />
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<tr><td><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ2WR-te-oBlOhNvUQduZ_cllsFREvjRbI96z4Z5PMMFHoU9zHzPL4yfibUrLjGnkcGIatPd7XQOtFVIriXwzN0aWm_mR4mrjGwEEfd3MFMBZwfMExNhgQvKy_10AH_-gWofrbW-hYHIA/s1600/%25CE%259F%25CE%259C%25CE%2599%25CE%25A7%25CE%259B%25CE%2597.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ2WR-te-oBlOhNvUQduZ_cllsFREvjRbI96z4Z5PMMFHoU9zHzPL4yfibUrLjGnkcGIatPd7XQOtFVIriXwzN0aWm_mR4mrjGwEEfd3MFMBZwfMExNhgQvKy_10AH_-gWofrbW-hYHIA/s1600/%25CE%259F%25CE%259C%25CE%2599%25CE%25A7%25CE%259B%25CE%2597.gif" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><b style="text-align: justify;"><span style="color: blue;">Ομίχλη</span></b><b style="text-align: justify;"> ονομάζεται το νέφος που επικάθεται στην επιφάνεια της Γης και προκαλεί ελάττωση της οριζόντιας ορατότητας σε αποστάσεις μικρότερες των 1.000 μ.</b></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Το νέφος της ομίχλης αποτελείται κυρίως από μικρά υδροσταγονίδια που έχουν σχηματιστεί από τη συμπύκνωση υδρατμών.Συνεπώς,για να σχηματιστεί ομίχλη,απαραίτητη προϋπόθεση είναι η παρουσία πολλών πυρήνων συμπύκνωσης και ο αέρας να είναι κορεσμένος από υδρατμούς (δηλαδή σχετική υγρασία <b>100%</b>).</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9lsSv-QxUarbnTxxWq919Rkr6R9bv5YbVq8oibzIYDAR9tNOGKDnkgoYDp6hEk40Cw7c6cvhBB378aTazh88uKWLNQZsHZb7uCndaOSFNBHJWmo-2m0O6958b5pv3fUFF6AxzTnwOIXc/s1600/%25CE%25A4%25CE%25BF+%25CE%25BD%25CE%25AD%25CF%2586%25CE%25BF%25CF%2582+%25CF%2584%25CE%25B7%25CF%2582+%25CE%25BF%25CE%25BC%25CE%25AF%25CF%2587%25CE%25BB%25CE%25B7%25CF%2582+%25CE%25B1%25CF%2580%25CE%25BF%25CF%2584%25CE%25B5%25CE%25BB%25CE%25B5%25CE%25AF%25CF%2584%25CE%25B1%25CE%25B9+%25CE%25BA%25CF%2585%25CF%2581%25CE%25AF%25CF%2589%25CF%2582+%25CE%25B1%25CF%2580%25CF%258C+%25CE%25BC%25CE%25B9%25CE%25BA%25CF%2581%25CE%25AC+%25CF%2585%25CE%25B4%25CF%2581%25CE%25BF%25CF%2583%25CF%2584%25CE%25B1%25CE%25B3%25CE%25BF%25CE%25BD%25CE%25AF%25CE%25B4%25CE%25B9%25CE%25B1+%25CF%2580%25CE%25BF%25CF%2585+%25CE%25AD%25CF%2587%25CE%25BF%25CF%2585%25CE%25BD+%25CF%2583%25CF%2587%25CE%25B7%25CE%25BC%25CE%25B1%25CF%2584%25CE%25B9%25CF%2583%25CF%2584%25CE%25B5%25CE%25AF+%25CE%25B1%25CF%2580%25CF%258C+%25CF%2584%25CE%25B7+%25CF%2583%25CF%2585%25CE%25BC%25CF%2580%25CF%258D%25CE%25BA%25CE%25BD%25CF%2589%25CF%2583%25CE%25B7+%25CF%2585%25CE%25B4%25CF%2581%25CE%25B1%25CF%2584%25CE%25BC%25CF%258E%25CE%25BD.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9lsSv-QxUarbnTxxWq919Rkr6R9bv5YbVq8oibzIYDAR9tNOGKDnkgoYDp6hEk40Cw7c6cvhBB378aTazh88uKWLNQZsHZb7uCndaOSFNBHJWmo-2m0O6958b5pv3fUFF6AxzTnwOIXc/s1600/%25CE%25A4%25CE%25BF+%25CE%25BD%25CE%25AD%25CF%2586%25CE%25BF%25CF%2582+%25CF%2584%25CE%25B7%25CF%2582+%25CE%25BF%25CE%25BC%25CE%25AF%25CF%2587%25CE%25BB%25CE%25B7%25CF%2582+%25CE%25B1%25CF%2580%25CE%25BF%25CF%2584%25CE%25B5%25CE%25BB%25CE%25B5%25CE%25AF%25CF%2584%25CE%25B1%25CE%25B9+%25CE%25BA%25CF%2585%25CF%2581%25CE%25AF%25CF%2589%25CF%2582+%25CE%25B1%25CF%2580%25CF%258C+%25CE%25BC%25CE%25B9%25CE%25BA%25CF%2581%25CE%25AC+%25CF%2585%25CE%25B4%25CF%2581%25CE%25BF%25CF%2583%25CF%2584%25CE%25B1%25CE%25B3%25CE%25BF%25CE%25BD%25CE%25AF%25CE%25B4%25CE%25B9%25CE%25B1+%25CF%2580%25CE%25BF%25CF%2585+%25CE%25AD%25CF%2587%25CE%25BF%25CF%2585%25CE%25BD+%25CF%2583%25CF%2587%25CE%25B7%25CE%25BC%25CE%25B1%25CF%2584%25CE%25B9%25CF%2583%25CF%2584%25CE%25B5%25CE%25AF+%25CE%25B1%25CF%2580%25CF%258C+%25CF%2584%25CE%25B7+%25CF%2583%25CF%2585%25CE%25BC%25CF%2580%25CF%258D%25CE%25BA%25CE%25BD%25CF%2589%25CF%2583%25CE%25B7+%25CF%2585%25CE%25B4%25CF%2581%25CE%25B1%25CF%2584%25CE%25BC%25CF%258E%25CE%25BD.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;"><span style="text-align: justify;"><span style="color: purple; font-family: "verdana" , sans-serif; font-size: small;"><b>Το νέφος της ομίχλης αποτελείται κυρίως από μικρά υδροσταγονίδια που έχουν σχηματιστεί από τη συμπύκνωση υδρατμών</b></span></span></td></tr>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Υπάρχουν όμως περιπτώσεις,κυρίως σε βιομηχανικές περιοχές,κατά τις οποίες οι πυρήνες συμπύκνωσης της ομίχλης περιέχουν και ποσότητες διάφορων ενώσεων του θείου,το οποίο προκύπτει από τις καύσεις των εργοστασίων.Έτσι η σχετική υγρασία της ομίχλης είναι μικρότερη από <b>100.</b></span><br />
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<span style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">ΤΥΠΟΙ ΟΜΙΧΛΗΣ</span></b></span><br />
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<span style="font-family: verdana, sans-serif;"><b> </b>Οι ομίχλες διακρίνονται σε δύο γενικές κατηγορίες,ανάλογα με τον τρόπο κατά τον οποίο σχηματίζονται:</span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">α) </span><span style="color: blue;">σε ομίχλες εξάτμισης </span>και </b></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">β) </span><span style="color: blue;">σε ομίχλες ψύξης.</span></b></span><br />
<span style="font-family: "verdana" , sans-serif;"><b> Ο</b></span><b style="font-family: verdana, sans-serif; line-height: 1.5em;">ι πρώτες σχηματίζονται από τον εμπλουτισμό του αέρα με μεγάλες ποσότητες υδρατμών οι οποίες προέρχονται από την εξάτμιση υγρού εδάφους, υδάτινων επιφανειών κ.ά.,ενώ οι δεύτερες σχηματίζονται από την ψύξη του αέρα,μέχρις ότου αποκτήσει τη θερμοκρασία δρόσου.</b><br />
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><span style="color: red; font-weight: bold;"> </span>Οι ομίχλες εξάτμισης διακρίνονται σε δύο τύπους: </span></div>
<b style="font-family: verdana, sans-serif; line-height: 1.5em;"><span style="color: red;">α)</span></b><b style="font-family: verdana, sans-serif; line-height: 1.5em;"><span style="color: blue;"> τις ομίχλες καπνού (steam fogs) </span>και<span style="color: blue;"> </span></b></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b><span style="color: red;">β)</span><span style="color: blue;"> τις μετωπικές ομίχλες (frontal fogs).</span></b></span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Οι ομίχλες καπνού σχηματίζονται όταν υπάρχει έντονη εξάτμιση από μια υδάτινη και αρκετά θερμή επιφάνεια σε ψυχρό αέρα. Τότε οι υδρατμοί συμπυκνώνονται πολύ γρήγορα και σχηματίζουν υδροσταγονίδια,τα οποία δεν μπορούν να απομακρυνθούν πολύ από την επιφάνεια εξάτμισης,γιατί σε μικρό ύψος απ' αυτή συμβαίνει αναστροφή της θερμοκρασίας λόγω της μεταφοράς θερμότητας προς τα πάνω.Τέτοιες ομίχλες σχηματίζονται συχνά κοντά σε λίμνες και ποταμούς μέσου πλάτους,κυρίως το φθινόπωρο,οπότε υπάρχουν οι κατάλληλες συνθήκες.Ειδικός τύπος τέτοιας ομίχλης σχηματίζεται το χειμώνα στις αρκτικές θαλάσσιες περιοχές.Αυτές οι ομίχλες έχουν μεγάλη ένταση και το ύψος τους μπορεί να φτάσει τα <b>1.600 μ</b>.,ενώ μοιάζουν πολύ με νέφη σωρειτών (<b>Cu</b>).Ονομάζονται αρκτικοί θαλάσσιοι καπνοί.</span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Οι μετωπικές ομίχλες σχηματίζονται κατά την πτώση θερμών σταγόνων βροχής και το πέρασμά τους ανάμεσα από ευσταθή στρώματα ψυχρού αέρα.Έτσι εμφανίζεται το φαινόμενο του υπερκορεσμού,γιατί συμβαίνει εξάτμιση των θερμών σταγόνων προς τον ψυχρό αέρα.Τέτοιες ομίχλες σχηματίζονται κοντά σε ψυχρές και θερμές μετωπικές επιφάνειες.</span><br />
<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> Οι ομίχλες ψύξης διαιρούνται σε πέντε τύπους:</span></div>
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<span class="Apple-style-span" style="color: blue; font-family: "verdana" , sans-serif;"><b><span style="color: red;">α)</span><span style="color: blue;"> μεταφοράς, </span></b></span><br />
<span class="Apple-style-span" style="color: blue; font-family: "verdana" , sans-serif;"><b><span style="color: red;">β)</span><span style="color: blue;"> ακτινοβολίας, </span></b></span><br />
<span class="Apple-style-span" style="color: blue; font-family: "verdana" , sans-serif;"><b><span style="color: red;">γ)</span><span style="color: blue;"> αναστροφής, </span></b></span><br />
<span class="Apple-style-span" style="color: blue; font-family: "verdana" , sans-serif;"><b><span style="color: red;">δ)</span><span style="color: blue;"> ανάμειξης, </span></b></span><br />
<span class="Apple-style-span" style="color: blue; font-family: "verdana" , sans-serif;"><b><span style="color: red;">ε) </span><span style="color: blue;">ανολίσθησης </span>ή<span style="color: blue;"> κλιτύος.</span></b></span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b><span style="color: blue;">Οι ομίχλες μεταφοράς </span>σχηματίζονται,όταν μεταφέρεται υγρός αέρας σε ψυχρότερες επιφάνειες,με αποτέλεσμα να παγώσει ο αέρας από κάτω και να αποκτήσει θερμοκρασία μικρότερη από τη θερμοκρασία δρόσου.</b>Ο αέρας πρέπει οπωσδήποτε να βρίσκεται σε κίνηση,οπότε κοντά στην επιφάνεια του εδάφους σχηματίζονται στροβιλοειδείς κινήσεις με αποτέλεσμα η ομίχλη μεταφοράς να έχει τη μεγαλύτερη πυκνότητά της στο ύψος στο οποίο φτάνουν οι κινήσεις αυτές.Όλες οι θαλάσσιες ομίχλες είναι ομίχλες μεταφοράς,εκτός από την περίπτωση του θαλάσσιου καπνού.Το χειμώνα οι ομίχλες μεταφοράς σχηματίζονται πάνω από παγωμένες ή χιονισμένες εκτάσεις στις οποίες μπαίνει από τη θάλασσα θερμός και υγρός αέρας,ενώ το καλοκαίρι οι ομίχλες μεταφοράς σχηματίζονται κυρίως πάνω από ψυχρές υδάτινες επιφάνειες προς τις οποίες μετατοπίζονται θερμές και υγρές μάζες αέρα.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> <span style="color: blue;">Οι ομίχλες ακτινοβολίας</span> σχηματίζονται όταν στάσιμες ποσότητες υγρού αέρα εφάπτονται με την επιφάνεια του εδάφους,η οποία κατά τη διάρκεια της νύχτας παγώνει λόγω ακτινοβολίας.</b>Έτσι παγώνουν και τα κάτω στρώματα του αέρα με αποτέλεσμα την εμφάνιση μιας αναστροφής της θερμοκρασίας της επιφάνειας σε μικρό ύψος.Το πάχος της αναστροφής ποικίλλει ανάλογα με τις αναταράξεις που συμβαίνουν και έτσι,όταν έχουμε άπνοια οι αναταράξεις είναι σχεδόν ανύπαρκτες και το πάχος της ομίχλης είναι μικρό.Τέτοιες ομίχλες σχηματίζονται κυρίως σε κοιλάδες και επίπεδες βαλτώδεις περιοχές στις οποίες λιμνάζουν ψυχρές μάζες αέρα.Σχηματίζονται επίσης και πάνω από βιομηχανικές περιοχές αυτές είναι πολύ πυκνές και ανθυγιεινές,γιατί περιέχουν προσμείξεις καπνού και άλλων προϊόντων που προέρχονται από τις καύσεις.</span><br />
<span style="font-family: "verdana" , sans-serif;"><span style="color: blue;"> </span><span style="color: blue; font-weight: bold;">Οι ομίχλες αναστροφής</span><b> σχηματίζονται στις πάνω επιφάνειες υγρών στρωμάτων αέρα λόγω της παρουσίας αναστροφής θερμοκρασίας.</b></span><span style="font-family: "verdana" , sans-serif;">Μερικές φορές η αναστροφή ενισχύεται από καθοδικές κινήσεις του αέρα με ταυτόχρονη ψύξη του πάνω στρώματος του υγρού αέρα με αποτέλεσμα τη δημιουργία νεφών </span><b style="font-family: verdana, sans-serif;">τύπου Stratus</b><span style="font-family: "verdana" , sans-serif;">.Τέτοιες ομίχλες είναι συχνές στις δυτικές ακτές των ηπείρων των υποτροπικών περιοχών κατά το καλοκαίρι.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b><span style="color: blue;">Οι </span><span style="color: blue;">ομίχλες ανάμειξης </span>σχηματίζονται όταν ανακατεύονται θερμές και ψυχρές αέριες μάζες,που περιέχουν μεγάλες ποσότητες υδρατμών.</b>Η μάζα του αέρα που προκύπτει από την ανάμειξη έχει θερμοκρασία μικρότερη της θερμοκρασίας δρόσου,οπότε προκύπτει συμπύκνωση των υδρατμών.Τέτοιες ομίχλες σχηματίζονται όταν συναντούνται θερμά με ψυχρά θαλάσσια ρεύματα.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"><b> <span style="color: blue;">Οι </span><span style="color: blue;">ομίχλες ανολίσθησης</span> ή <span style="color: blue;">κλιτύος</span> σχηματίζονται όταν συμβαίνει ανολίσθηση και αδιαβατική ψύξη υγρού αέρα,που μεταφέρεται από τους ανέμους στις προσήνεμες πλαγιές λόφων ή βουνών.</b>Η ομίχλη δημιουργείται όταν οι ανερχόμενες αέριες μάζες φτάσουν στη στάθμη κορεσμού τους.</span></div>
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<span class="Apple-style-span" style="font-family: "verdana" , sans-serif;"> <b><span style="color: blue;">Η ομίχλη χαρακτηρίζεται ως </span><span style="color: blue;">αχλύς (Mist)</span>,όταν η οριζόντια ορατότητα μέσα στη θολωμένη ατμόσφαιρα κυμαίνεται από 1 μέχρι 2 χλμ.</b>Όταν η οριζόντια ορατότητα είναι μεγαλύτερη από <b>2 χλμ</b>.,τότε έχουμε το φαινόμενο της ξερής αχλύος (<b>Haze</b>),ενώ όταν η ορατότητα είναι μεγαλύτερη του <b>1 χλμ.</b>,έχουμε την υγρή αχλύ (<b>Μist</b>).Στην πρώτη περίπτωση η αχλύς αποτελείται από μικρά σωμάτια σκόνης, που σηκώνεται από ξερές περιοχές,και από ξερά και μικρά μόρια χλωριούχου νατρίου.Στη δεύτερη περίπτωση η αχλύς αποτελείται από πολλά μικρά υδροσταγονίδια που σχηματίζουν αραιή ομίχλη.Ξεχωρίζει από την κανονική ομίχλη,γιατί έχει χρώμα υπόφαιο.</span></div>
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ΣΤΕΡΓΙΟΣ ΠΕΛΛΗΣhttp://www.blogger.com/profile/12469413560413402563noreply@blogger.com