A Golden Section, in mathematics, is the geometric proportion in which a line is divided so that the ratio of the length of the longer segment to the length of the entire line is equal to the ratio of the length of the shorter segment to the length of the longer segment.

A golden section is thus created by the point C on line AB when AC/AB = CB/AC. This ratio has a numerical value of 0.618…, and can be derived as follows: when AB = 1, and the length of AC = x, then AC/AB = CB/AC becomes x/1 = (1 - x)/x.

Some historians claim that the properties of the golden section helped the followers of the Greek mathematician and philosopher Pythagoras to discover the concept of incommensurable lines, the geometric equivalents of irrational numbers.

It is certain, however, that since late antiquity many philosophers, artists, and mathematicians have been intrigued by the Golden Section. During the Renaissance it was known as the divine proportion; and today it is widely accepted that architectural structures or geometric shapes that have sides following the pattern of this ratio display a special beauty.