Fibonacci Numbers and the Golden Ratio

Overview

Discover the fascinating mathematical patterns that appear throughout nature, art, and science in this exploration of Fibonacci numbers and the golden ratio.

Course No. 10470

This 12-lecture course with Professor Arthur T. Benjamin reveals:

• The simple yet profound Fibonacci sequence (0, 1, 1, 2, 3, 5, 8…)

• How the golden ratio (approximately 1.618) emerges from these numbers

• Surprising appearances in nature, from flower petals to spiral galaxies

• Applications in mathematics, art, architecture, and more

• Mathematical proofs and properties through engaging demonstrations

Through puzzles, magic tricks, and real-world examples, you’ll uncover why these concepts have fascinated mathematicians and artists for centuries.

Video Lectures

1. Puzzling Fibonacci Patterns (20 min)

2. Proving Perplexing Properties (25 min)

3. Applications of Fibonacci Numbers (28 min)

4. Fibonacci Numbers and Pascal’s Triangle (28 min)

5. A Favorite Fibonacci Fact (31 min)

• Fibonacci Numbers, Lucas Numbers, and Beyond (28 min)

7. The Mysterious Golden Ratio (31 min)

8. Phi: The Most Irrational Number (25 min)

9. A Golden Formula for Fibonacci (28 min)

10. The Golden Ratio and Geometry (27 min)

11. The Golden Ratio and Benford’s Law (27 min)

12. Fibonacci and the Golden Ratio Everywhere (32 min)