golden ratio

Also known as τ, Phi, Tau, φ, Φ, Τ, golden mean, golden section

ratio between two quantities whose sum is at the same ratio to the larger one

AI overview

The golden ratio is a special mathematical relationship where two quantities are sized so that their sum relates to the larger quantity in exactly the same way that the larger quantity relates to the smaller one. This proportion appears frequently in nature and art, which is why many people find it aesthetically pleasing and mathematically fascinating.

AI-generated from the Wikipedia summary — may contain errors.

~40 min read

Encyclopedic overview

A golden rectangle with long side a + b and short side a can be divided into two pieces: a similar golden rectangle (shaded red, right) with long side a and short side b and a square (shaded blue, left) with sides of length a. This illustrates the relationship ⁠a + b/a⁠ = ⁠a/b⁠ = φ.

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities ⁠

Excerpted from Wikipedia’s “golden ratio” article, available under the CC BY-SA 4.0 licence.