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Golden ratio

This calculator determines proportions according to golden ratio

This calculator determines proportions according to golden ratio. You can read about golden ration below the calculator

Created on PLANETCALC

Golden ratio

Digits after the decimal point: 8
Long
 
Short
 
Sum
 
Golden ratio
 



Golden ratio also known as the divine proportion, golden mean, or golden section is a term for dividing a segment so the long/short ratio is equal to all/long ratio.
\frac{a}{b}=\frac{a+b}{a}
This number is constant.
If we suppose that b is 1, a should be equal to golden ratio. Let's substitute it for x
\frac{x}{1}=\frac{x+1}{x}x=\frac{x+1}{x}x^2=x+1x^2-x-1=0

This is square equation. The positive root of the equation is
\frac{1+\sqrt{5}}{2}
and it is a golden ratio number
\frac{\sqrt{5}+1}{2}=1,6180339887...
It is irrational number.

The rough approximation of golden ratio is the long part is 0,62 of all, and short part is 0,38.

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