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In geometry, a golden rectangle is a rectangle with side lengths in golden ratio +:, or :, with approximately equal to 1.618 or 89/55. Golden rectangles exhibit a special form of self-similarity : if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well.
A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural objects and artificial systems such as financial markets , in some cases based on dubious fits to data. [ 8 ]
A supergolden rectangle is a rectangle whose side lengths are in a : ratio. Compared to the golden rectangle , the supergolden rectangle has one more degree of self-similarity . Given a rectangle of height 1 , length ψ {\displaystyle \psi } and diagonal length ψ 3 {\displaystyle {\sqrt {\psi ^{3}}}} (according to 1 + ψ 2 = ψ ...
Its true value is the real solution of the equation x 3 = 2x 2 + 1. The name supersilver ratio results from analogy with the silver ratio , the positive solution of the equation x 2 = 2 x + 1 , and the supergolden ratio .
The root-3 rectangle is also called sixton, [6] and its short and longer sides are proportionally equivalent to the side and diameter of a hexagon. [7] Since 2 is the square root of 4, the root-4 rectangle has a proportion 1:2, which means that it is equivalent to two squares side-by-side. [7] The root-5 rectangle is related to the golden ratio ...
Print/export Download as PDF; Printable version; In other projects Wikibooks; ... Equation 2}} (i.e., Equation 2). This template can be used together with ...
Consider a rectangle such that the ratio of its length L to its width W is the n th metallic ratio. If one remove from this rectangle n squares of side length W, one gets a rectangle similar to the original rectangle; that is, a rectangle with the same ratio of the length to the width (see figures).
The golden section is a line segment sectioned into two according to the golden ratio.The total length a+b is to the longer segment a as a is to the shorter segment b.. In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller.