Golden Section and Ratio

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Presentation transcript:

Golden Section and Ratio Researched by Alex Gray

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

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

Phi =1.618033988749895... Solution to a quadratic equation Dividing line in an extreme and mean ratio “P” =1.618 0339 887 … “p” =0.6180339887 …

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, ...

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

Sources http://www.goldennumber.net/neophite.htm http://www.mathsisfun.com/numbers/golden-ratio.html

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