Number Theory

    

A Theorem on the Golden Section and Fibonacci Numbers

Authors: Rolando Zucchini

In the chapter 12° of his most significant book LIBER ABACI, Leonardo Pisano known as Fibonacci (Pisa 1170-1240 (?)) proposed a problem on the reproduction of rabbits [*]. So many scholars deduced that he arrives to his famous numerical sequence starting from this problem. In this article is explained a new hypothesis. The Fibonacci sequence was generated by the iteration of a theorem on the Golden Section, and it is presumably that was the great Italian mathematician to state and demonstrate it. The theorem allow us to proof a lot of properties of Fibonacci numbers. [*] A man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced by the initial couple in a year supposing every couple each month produces a new pair that can reproduce itself from the second month?

Comments: 13 Pages.

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[v1] 2023-10-04 07:27:08

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