Fibonacci Numbers, Golden Section and Applications

TL;DR

This thesis explores Fibonacci numbers' mathematical properties, their occurrence in nature, geometry, and economics, and demonstrates their connection to the Golden section, prime numbers, and stock market analysis.

Contribution

It provides new proofs of mathematical identities involving the Golden section and Fibonacci numbers, and investigates their applications across various fields.

Findings

Golden section derived from Fibonacci numbers

Prime numbers' infinity proved using Fibonacci properties

Fibonacci numbers observed in nature and stock exchange

Abstract

In this thesis we examined mathematical properties of Fibonacci numbers and applications of this numbers in the nature,geometry and economy.We obtained Golden section and proved some mathematical identities using Golden section. Infinity of the prime numbers proved by using properties of Fibonacci numbers. Encounterings with Fibonacci numbers in the nature are examined with details. Also examples are given for relation about Fibonacci numbers and stock exchange and these are examined.