1. Golden Section and Ratio
Researched by Alex Gray

2. Discovery Unknown who truly discovered Phi Dates back before the 1800s
Egyptians and Greeks were first documented using it (1800s)

3. Background AKA Divine Proportion Ratio or proportion defined by Phi
Derived from geometric constructions
Relates back to the Fibonacci series

4. Phi =1.618033988749895... Solution to a quadratic equation
Dividing line in an extreme and mean ratio
“P” = … “p” = …

5. Fibonacci…12th Century Fibonacci Series:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …
Formulas:
fn = Phi ^n / 5½ … Starts n=0, 1, 2, 3, 4, …
fn = Phi ^n / (Phi + 2)... Starts n= 1, 2, 3, 4, ...

6. In Reality Phi appears in: The proportions of the living Plants DNA
The solar system
Art and architecture
Music
Population growth
The stock market
The Bible and in theology

7. Sources