golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618. It is the ratio of a line segment cut into two pieces of different lengths such that the ratio of the whole segment to that of the longer segment is equal to the ratio of the longer segment to the shorter segment. The origin of this number can be traced back to Euclid, who mentions it as the “extreme and mean ratio” in the Elements. In terms of present day algebra, letting the length of the shorter segment be one unit and the length of the longer segment be x units gives rise to the equation (x + 1)/x = x/1; this may be rearranged to form the quadratic equation x2 – x – 1 = 0, for which the positive solution is x = (1 + Square root of√5)/2, the golden ratio.

Definition courtesy of Encyclopedia Britannica