Golden Ratio
Golden Mean · Golden Section
A mathematical relationship where the ratio of two quantities equals the ratio of their sum to the larger of the two quantities (~1.618), a pattern that appears in natural environments including the spiral arrangement of leaves and other plant parts.
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Origin
The earliest known mathematical study appears in Euclid's Elements (circa 300 BCE), where he defined dividing a line into "extreme and mean ratio." The concept was important in the geometry of regular pentagrams and pentagons. Awareness may date earlier to Pythagorean mathematicians. In 1910, American mathematician Mark Barr popularized the Greek letter phi (φ) as its symbol, reportedly referencing Greek sculptor Phidias.
Updated February 22, 2026