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Volume 10, 2010

Zoran Lučić
Pages 82-90

Indivisible lines, Pythagoras’ theorem and Fibonacci sequence

According to Alexander of Aphrodisia Plato conducted investigation regarding existence of indivisible lines. Reading carefully passage of the Plato’s Republic, though it becomes clear that the presumption of the existence of indivisible lines would lead to the conclusion that the basic theorem of geometry — Pythagoras’ theorem — is not valid anymore. Moreover, “rational diameter of five” mentioned in Plato’s passage could be seven, as suggested by Theon, but also — eight. This gives a clue that Fibonacci numbers were possibly known to Greeks.