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reference.html
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<!Doctype html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>References</title>
</head>
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<body>
<header>
<h1>Golden Ratio!!</h1>
<h2>References</h2>
</header>
<div class="text">
<h3>Explanatory footnotes :</h3>
<ol>
<li>If the constraint on a and b each being greater than zero is lifted, then there are actually two solutions, one positive and one negative, to this equation. ϕ is defined as the positive solution. The sum of the two solutions is one, and the product of the two solutions is negative one.</li>
<li>Euclid, Elements, Book II, Proposition 11; Book IV, Propositions 10–11; Book VI, Proposition 30; Book XIII, Propositions 1–6, 8–11, 16–18.</li>
<li>
"῎Ακρον καὶ μέσον λόγον εὐθεῖα τετμῆσθαι λέγεται, ὅταν ᾖ ὡς ἡ ὅλη πρὸς τὸ μεῖζον τμῆμα, οὕτως τὸ μεῖζον πρὸς τὸ ἔλαττὸν."</li>
<li>
After Classical Greek sculptor Phidias (c. 490–430 BC); Barr later wrote that he thought it unlikely that Phidias actually used the golden ratio.</li>
<li>Not to be confused with the silver mean, also known as the silver ratio.</li>
<li>
Taylor translated Herodotus: "this Pyramid, which is four-sided, each face is, on every side 8 plethra, and the height equal." He interpreted this imaginatively, and in 1860, John Herschel was the first of many authors to repeat his false claim. In 2000, Roger Herz-Fischler traced the error back to Taylor.
</li>
</ol>
<h3> Works cited :</h3>
<ul>
<li>Livio, Mario (2003) [2002]. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number (First trade paperback ed.). New York City: Broadway Books. ISBN 978-0-7679-0816-0.</li>
<li>Stakhov, Alexey P.; Olsen, Scott (2009). The Mathematics of Harmony: From Euclid to Contemporary Mathematics and Computer Science. Singapore: World Scientific Publishing. ISBN 978-981-277-582-5.</li>
</ul>
<h3>Further reading</h3>
<ul>
<li>Doczi, György (2005) [1981]. The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture. Boston: Shambhala Publications. ISBN 978-1-59030-259-0.</li>
<li>Hemenway, Priya (2005). Divine Proportion: Phi In Art, Nature, and Science. New York: Sterling. ISBN 978-1-4027-3522-6.</li>
<li>Huntley, H. E. (1970). The Divine Proportion: A Study in Mathematical Beauty. New York: Dover Publications. ISBN 978-0-486-22254-7.</li>
<li>Joseph, George G. (2000) [1991]. The Crest of the Peacock: The Non-European Roots of Mathematics (New ed.). Princeton, NJ: Princeton University Press. ISBN 978-0-691-00659-8.</li>
<li>Sahlqvist, Leif (2008). Cardinal Alignments and the Golden Section: Principles of Ancient Cosmography and Design (3rd Rev. ed.). Charleston, SC: BookSurge. ISBN 978-1-4196-2157-4.</li>
<li>Schneider, Michael S. (1994). A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science. New York: HarperCollins. ISBN 978-0-06-016939-8.</li>
<li>Scimone, Aldo (1997). La Sezione Aurea. Storia culturale di un leitmotiv della Matematica. Palermo: Sigma Edizioni. ISBN 978-88-7231-025-0.</li>
<li>Walser, Hans (2001) [Der Goldene Schnitt 1993]. The Golden Section. Peter Hilton trans. Washington, DC: The Mathematical Association of America. ISBN 978-0-88385-534-8.</li>
</ul>
</div>
</body>
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