Take a line AB and divide it by C so that the ratio AC:CB=AB:AC. It works out at approximately 8/13. This mathematical proportion is considered to be beautiful.

The ideal proportion according to the ancient Greeks. Visualized as the division of a line into two unequal segments in such a way that the ratio of the smaller segment to the larger segment is equal to the ratio of the larger to the whole. It is usually defined as 21:34, that is, 21/34 and 34/(21+34) both equal approximately 0.618. A rectangle whose sides are of this proportion is called a "golden rectangle". Golden rectangles can be found in the proportions of the Parthenon and many medieval manuscripts.

Any length divided so that the ratio of the smaller to the larger part is equivalent to the ratio between the larger part and the whole and is always 0.618.

the proportional relation between two divisions of line or two dimension of a plane figure such that short : long :: long : (short + long)

an area that has a specific ratio of height to width to depth

A traditional proportional system for visual harmony expressed when a line or area is divided into two so that the smaller.part is to the larger as the larger is to the whole. The ratio developed is 1:1.6180....or, roughly, 8:13.

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.

(also called golden ratio or divine proportion) the division of a line segment into two segments such that the ratio of the whole segment, to the longer part is the same as the ratio of the longer part to the shorter part. This ratio, expressed mathematically is 1: 1.61803

A ratio of height to width to length of a room to achieve "good acoustics" and first recommended by the ancient Greeks. The ratio is approximately the width 1.6 times the height and the length 2.6 times the height