2008•ACM communications in computer algebraRequires access

Dethroning Fibonacci Sequence (abstract only)

Michael A. Kelsey

Abstract

The purpose of this presentation is to demonstrate some properties and applications of Fibonacci numbers. We present Binet's Formula and its proof. By using Binet's Formula, we show that the Fibonacci sequence is not a special sequence. The Fibonacci sequence has a closed form solution which can be expressed analytically in terms of a bounded number of certain "well-known" functions, which indicates that the Fibonacci sequence is not unique.

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Key concepts: Fibonacci number, Sequence (biology), Fibonacci polynomials, Pisano period, Lucas number, Mathematics, Combinatorics, Lucas sequence