The relations between Fibonacci numbers and Pascal's triangle

This thesis consists of five chapters. In the first chapter, the historical background of Fibonacci numbers and the definitions of both Fibonacci numbers and the Golden ratio are given. In the second chapter of the thesis, some well known identities that Fibonacci numbers satisfy and the problems that can be solved by using Fibonacci numbers are shown. The importance of Fibonacci numbers and the Golden ratio is mentioned. In the third chapter of the thesis, the basic statements about Pascal's Triangle and Binomial Expansion are given. After that the relation between Fibonacci numbers and Pascal's Triangle is found. In the forth chapter of the thesis, Hosoya's triangle and Catalan triangle, which have similar structures as Pascal's triangle are defined. And finally, starting with Fibonacci numbers, it was discovered a Pascal-like triangle which has a recurrence relation of its own. In the last chapter of the thesis, the result is given.