Golden ratio

What's the Golden ratio?

The golden line / rectangle is for the eye the best ratio.
You find this ratio in nature and in the best designs. Get inspired!

Get inspired!

The golden ratio is an irrational mathematical constant.

= 1.6180339887
= 0.6180339887

Explanation Golden ratio line:

Point (S) on the line A to B divided the line in two
"Golden Sections"

The golden line ratio A to S to B.
*S1 is mirror point from S



In this website the golden ratio is denoted by the Greek lowercase letter phi (): 1.6180339887, while its inverse, (1/phi), which is also equal to (phi-1), or 0.6180339887... is denoted by the uppercase variant Phi .

The figure on the right illustrates the geometric relationship that defines this constant. Expressed algebraically:



This equation has one positive solution in the algebraic irrational number


Golden ratio conjugate



The negative root of the quadratic equation for φ(the "conjugate root") is 1/Φ = 1- Φ -0.618.
The absolute value of this quantity (0.618) corresponds to the length ratio taken in reverse order (shorter segment length over longer segment length, b/a), and is sometimes referred to as the golden ratio conjugate.It is denoted here by the capital Phi (Φ):

Explanation Golden ratio Rectangle:

Golden rectangle construction:
1) Construct a square (green).
2) Draw a cirle from the midpoint M opposite corner C and R.
3) Extend line A,S to B.
4) Defines the long dimension of the rectangle point B.

Explanation Golden ratio Eye point:

Next to the square shows up a new golden rectangle. You see a endlessly repeating.

Golden place:

The ideal place in the golden rectangle for example a person.

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