Module 2: The Fibonacci Sequence & The Golden Ratio

1. Fibonacci **Sequence**

1.1. Leonardo Pisano

1.1.1. **personal life**

1.1.1.1. Pisa, Italy; 1170

1.1.1.2. fillius Bonacci/ son of Bonacci (Guglielmo Bonaccio)

1.1.2. **advocacies to math**

1.1.2.1. advocated the use of the digits 0 to 9 and of the place values

1.1.2.2. recognized + well-known for popularizing the Hindu-Arabic numeral system or decimal system in Europe

1.1.2.3. discovered the Fibonacci sequence via breeding of rabbits

1.2. nature, phenomena, human body, **photographs**

1.3. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,...

2. The Golden Ratio

2.1. **Symbols**

2.1.1. ϕ phi (uppercase letter)

2.1.2. varphi (lowercase letter)

2.2. **Phidias**

2.2.1. Greek sculptor

2.3. equal to...

2.3.1. **approx. 1.618**

2.3.2. **V5+1 / 2**

2.3.3. **=2(sin 54)**

2.4. Divine Ratio/ Divine Proportion

2.5. artworks + creative designs of many artists + architects

2.5.1. **The Golden Spiral**

2.5.2. **The Golden Rectangle**

2.5.3. **Proportions of the human body**

3. The bigger Fibonacci numbers is used as a ratio, the closer you get to the approx. value of the Golden Ratio.