User:Finell

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Steven Finell

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extreme and mean ratio (the principal term used from the 3rd century BC until the 18th century),Cite error: The <ref> tag has too many names (see the help page).


The first calculation of the golden ratio was described by Euclid in his Elements (Greek: Στοιχεῖα)

Euclid's Elements (Greek: Στοιχεῖα) gives the first known written definition of the golden ratio: "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less."Cite error: The <ref> tag has too many names (see the help page). Euclid explains a construction for cutting (sectioning) a line "in extreme and mean ratio", i.e. the golden ratio.]]),[1] Throughout the Elements, several propositions (theorems in modern terminology) and thier proofs employ the golden ratio.[2]


http://aleph0.clarku.edu/~djoyce/java/elements/toc.html

http://farside.ph.utexas.edu/euclid/euclid.pdf


Euclid (David E. Joyce, ed. 1997) [3rd century BC]. Elements. Retrieved 2006-08-30. {{cite book}}: Check date values in: |year= (help) Citations in the text are to this online edition.



[3]


Another

  1. ^ Euclid, Elements, Book 6, Proposition 30.
  2. ^ Euclid, Elements, Book 2, Proposition 11; Book 4, Propositions 10–11; Book 13, Propositions 1–6, 8–11, 16–18.
  3. ^ Hemenway, Priya (2005). Divine Proportion: Phi In Art, Nature, and Science. New York: Sterling. pp. 20–21. ISBN 1-4027-3522-7.



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