Saltar al contenido principal Saltar al cuadro de búsqueda
Summary Article: Golden Section
From The Columbia Encyclopedia

in mathematics, division of a line segment into two segments such that the ratio of the original segment to the larger division is equal to the ratio of the larger division to the smaller division. If c is the original segment, b is the larger division, and a is the smaller division, then c = a + b and c/b = b/a. Thus, b is the geometric mean of a and c; the ratio is known as the Divine Proportion. The Golden Rectangle, whose length and width are the segments of a line divided according to the Golden Section, occupies an important position in painting, sculpture, and architecture, because its proportions have long been considered the most attractive to the eye. The constructions of regular polygons of 5, 10, and 15 sides depend on the division of a line by the Golden Section. The numerical ratio of the greater segment of the line to the shorter segment as determined by the Golden Section is symbolized by the Greek letter phi and has the approximate value 1.618. It occurs in many widely varying areas of mathematics. For example, in the Fibonacci sequence (the sequence of numbers formed by adding successive members to find the next member—0, 1, 1, 2, 3, 5, 8, 13, … ), the values of the ratios 1, 2/1, 3/2, 5/3, 8/5, 13/8, … approach the value of the Golden Section.

  • See Huntley, H. E. , The Divine Proportion (1970).
The Columbia Encyclopedia, © Columbia University Press 2018

Related Articles

Full text Article golden section
Merriam-Webster's Collegiate(R) Dictionary

(1875) : a proportion (as one involving a line divided into two segments or the length and width of a rectangle and their sum) in which the ratio of

Full text Article golden rectangle
A/V A to Z: An Encyclopedic Dictionary of Media, Entertainment and Other Audiovisual Terms

A rectangle where the ratio of the long side to the short side is the golden ratio (φ, or approximately 1.618:1). In practice, most objects based on

Full text Article Golden Section
Bloomsbury Guide to Human Thought

Golden Section (or Golden Mean) was the 19th-century name given to a system of mathematical proportion, which had been discussed since ancient...

Ver más de Credo