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Golden ratio

This calculator determines proportions according to golden ratio

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

PLANETCALC, Golden ratio

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+1
x^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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