An Etymological Dictionary of Astronomy and Astrophysics
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1) The number giving the position of any year in the lunar or → Metonic cycle of about 19 years. Each year has a golden number between 1 and 19. It is found by adding 1 to the given year and dividing by 19; the remainder in the division is the golden number. If there is no remainder the golden number is 19 (e.g., the golden number of 2007 is 13).
2) Same as → golden ratio.

Golden, adj. of → gold; → number.

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.

→ golden; → ratio.