golden section

The division of a line into two segments so that the ratio of the whole line to the larger segment equals the ratio of larger segment to the smaller one; often called the golden section. This ratio was once considered by some as having an inherent aesthetic value.

Golden section, also called the divine proportion, is the division of a line segment so that the ratio of the whole segment to the larger part is equal to the ratio of the larger part to the smaller part. The ratio is approximately 1.61803 to 1. The number 1.61803 is called the Golden Number (also called Phi [with a capital P]). The golden number is the limit of the ratios of consecutive Fibonacci numbers, such as, for instance, 21/13, and 34/21. A golden rectangle is one whose length and width correspond to this ratio. The ancient Greeks thought this shape had the most pleasing proportions. Many famous painters have used the Golden Rectangle in their paintings, and architects have used it in their design of buildings, the most famous example being the Greek Parthenon.

A mathematical proportion where the ratio between a small section and a larger section is equal to the ratio between the larger section and both sections put together. Used by many 20th century composers, especially Bela Bartok, to determine the point of climax for a given work.