Fibonacci Numbers and the Golden Ratio

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88 pages
This book consists of the lecture notes, problems and solutions from the Coursera course “Fibonacci numbers and the golden ratio.” Links are provided to the videos used in the course.
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About the author

Dr. Jeffrey Chasnov received his BA from UC Berkeley in 1983, and his PhD from Columbia University in 1990. He had postdoctoral appointments at NASA, Stanford University, and the Université Joseph Fourier before expatriating to Hong Kong in 1993, where he is currently a Professor of Mathematics at t...


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.

  1. The Fibonacci sequence 
  2. The Fibonacci sequence redux 
  3. The golden ratio 
  4. Fibonacci numbers and the golden ratio 
  5. Binet’s formula 
  6. The Fibonacci Q-matrix 
  7. Cassini’s identity 
  8. The Fibonacci bamboozlement 
  9. Sum of Fibonacci numbers 
  10. Sum of Fibonacci numbers squared 
  11. The golden rectangle 
  12. Spiraling squares 
  13. The golden spiral 
  14. An inner golden rectangle 
  15. The Fibonacci spiral 
  16. Fibonacci numbers in nature 
  17. Continued fractions 
  18. The golden angle 
  19. The growth of a sunflower 

Congratulations to Prof. Chasnov for his amazing course and book. An extremely rare opportunity for someone interested in the beauty of Mathematics.
October 7, 2018 at 1:02 PM
A great book about Fibonacci Numbers and associated topics. It is well explained and includes a lot of exercises. It was very helpful for me during the course.
September 24, 2018 at 8:46 AM
Very good material on the topics of Fibonacci ratio and other related topics. I found it a little too concise, however, it covered all the needs of the course it accompanied. Quite a good read standalone as well. If only it contained a little more material and info, it would have been even better.
August 28, 2018 at 1:50 PM
So much fun and so interesting!
May 13, 2018 at 1:57 PM
Excellent! Very clear explanations, very helpful drawings and diagrams, most informative and interesting!
April 25, 2018 at 11:13 PM
Very good explanations with many exercises to apply knowledge. Links mathematical analysis to natural phenomena... really interesting! Step-by-step, making it easy to work through. Some challenging problems, which makes the whole experience more rewarding. Definitely recommended!
March 26, 2018 at 9:21 AM
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