Chasnov Jeffrey R. Fibonacci Numbers and the Golden Ratio

Bookboon, 2016. — 88 p. — ISBN: 978-87-403-1559-2.This book consists of the lecture notes, problems and solutions from the author’s Coursera course “Fibonacci numbers and the golden ratio.” YouTube links to the course’s videos are provided at the top of each lecture. In these lectures, we learn the origin of the Fibonacci numbers and the golden ratio, and derive a formula to compute any Fibonacci number from powers of the golden ratio. We learn how to add a series of Fibonacci numbers and their squares, and unveil the mathematics behind a famous paradox called the Fibonacci bamboozlement. We construct a beautiful golden spiral and an even more beautiful Fibonacci spiral, and we learn why the Fibonacci numbers can appear unexpectedly in nature. At the end of each lecture, students are given interesting problems to solve, and the author’s detailed solutions are provided in the book’s Appendix.The Fibonacci sequence
The Fibonacci sequence redux
The golden ratio
Fibonacci numbers and the golden ratio
Binet’s formula
The Fibonacci Q-matrix
Cassini’s identity
The Fibonacci bamboozlement
Sum of Fibonacci numbers
Sum of Fibonacci numbers squared
The golden rectangle
Spiraling squares
The golden spiral
An inner golden rectangle
The Fibonacci spiral
Fibonacci numbers in nature
Continued fractions
The golden angle
The growth of a sunflower.