The golden ratio explained — why it appears in art, nature and design

The golden ratio (approximately 1.618, represented by the Greek letter φ, phi) is a mathematical ratio found throughout art, architecture, design and nature. Two quantities are in the golden ratio when their ratio is the same as the ratio of their sum to the larger of the two quantities.

Where it appears

• Nature: the spiral of a nautilus shell, the arrangement of sunflower seeds, the branching of trees and the proportions of the human face
• Art and architecture: the Parthenon, Leonardo da Vinci's Vitruvian Man, many Renaissance paintings
• Design: the proportions of the A4 paper size (and other A-series sizes) closely approximate the golden ratio — which is why documents scaled from A4 to A3 or A5 maintain their proportions

Why designers use it

Compositions built on golden ratio proportions are often described as inherently pleasing or harmonious. Whether this reflects a genuine perceptual preference or cultural conditioning is debated. Practically, the rule of thirds (dividing an image into a 3×3 grid) is a simplified approximation of the golden ratio used in photography and visual design.