Monday, July 26, 2010

The Pentagon and the Golden Section

The cosine of 144° in magnitude equals 1/2 the golden ratio, φ, which was used in the construction of the pentagon. Euclid in his Elements, circa 300 B.C., also uses the golden ratio to construct the pentagon. See Euclid, Elements, Book IV, Propositions 10-11. But Eudoxus, an astronomer and a contemporary of Plato, is given credit for discovery of the golden section which defines the golden ratio. Much of the content of Euclid's Elements was known to the Pythagoreans who shared their knowledge with the Athenian philosophers.

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