An Etymological Dictionary of Astronomy and Astrophysics

If a line segment is divided into a larger subsegment (a) and a smaller subsegment (b), when the larger subsegment is related to the smaller exactly as the whole segment is related to the larger segment, i.e. a/b = (a + b)/a. The golden ratio, a/b is usually represented by the Greek letter φ. It is also known as the divine ratio, the golden mean, the → golden number, and the golden section. It was believed by Greek mathematicians that a rectangle whose sides were in this proportion was the most pleasing to the eye. Similarly, the ratio of the radius to the side of a regular → decagon has this proportion. The numerical value of the golden ratio, given by the positive solution of the equation φ² - φ - 1 = 0, is φ = (1/2)(1 + √5),
approximately 1.618033989. The golden ratio is an → irrational number. It is closely related to the → Fibonacci sequence.

See also: → golden; → ratio.