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Fibonacci Numbers and the Golden Ratio

Fibonacci Numbers and the Golden Ratio
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ISBN: 978-87-403-1559-2
1 edition
Pages : 88
  • Price: 129.00 kr
  • Price: €13.99
  • Price: £13.99
  • Price: ₹250
  • Price: $13.99
  • Price: 129.00 kr
  • Price: 129.00 kr

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About the book

  1. Description
  2. Content

Description

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.

Content

  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 

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