Introduction to Fibonacci Numbers and the Golden Ratio

• Main Authors: Li,Zong-Han, 李宗翰
• Other Authors: 曾勵新
• Format: Others
• Language: zh-TW
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/mx4h5v

碩士 === 逢甲大學 === 應用數學系 === 107 === We all know that the Fibonacci numbers are a famous sequence. But do you really know how it came from? Can you identify some of its interesting properties? Do you know its relationship with the so-called Golden ratio? This paper introduces the origin of the Fibonacci numbers, and derives the general formula of the Fibonacci numbers through several methods. Then we use the general formula to verify some of the important properties, including and the relationship between the Fibonacci numbers and the gold ratio. To demonstrate the power of the applications of Fibonacci numbers, we give the Fibonacci search algorithm and the golden section search method as two examples. Finally we find some sequences that are closely related to the Fibonacci numbers, which shows there are still many areas on which we can do further study.