The Greek letter phi, written φ or ϕ, commonly represents the golden ratio. This irrational number is approximately 1.618 and is defined as (1 + √5) / 2.
The golden ratio describes a division in which the ratio of the whole length to the longer part equals the ratio of the longer part to the shorter part. Ancient Greek mathematicians called this construction the “extreme and mean ratio,” and Euclid described it in Elements. It also appears in the geometry of regular pentagons and pentagrams.
The symbol φ was introduced for the golden ratio in the early 20th century, with mathematician Mark Barr often credited with popularising it around 1910. The letter is sometimes linked to the Greek sculptor Phidias, although there is no evidence that Phidias himself used the ratio. The golden ratio is also connected to Fibonacci numbers, whose successive ratios approach 1.618.