The golden ratio (φ ≈ 1.618) is a mathematical constant where the ratio of the whole to the larger part equals the ratio of the larger part to the smaller part.
The golden ratio satisfies φ = (1 + √5)/2 ≈ 1.6180339887. Two quantities a > b are in the golden ratio if (a+b)/a = a/b = φ. The golden ratio appears in geometry (pentagons, golden rectangles), art (Renaissance paintings), architecture (Parthenon), and nature (shell spirals, flower petals). It is often considered aesthetically pleasing and is used in design and photography.
The golden ratio was studied by Greek mathematicians, particularly Euclid who described it as "extreme and mean ratio" in his "Elements" (300 BCE). The term "golden section" was used by German mathematician Martin Ohm in 1835. The symbol φ was first used by American mathematician Mark Barr in the early 1900s, named after the Greek sculptor Phidias.