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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 ]
Construction of a golden rectangle Construct a simple square; Draw a line from the midpoint of one side of the square to an opposite corner; Use that line as the radius to draw an arc that defines the height of the rectangle; Use the endpoints of the arc to complete the rectangle; The proportions of the resulting rectangle is φ or
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For example, a golden spiral can be approximated by first starting with a rectangle for which the ratio between its length and width is the golden ratio. This rectangle can then be partitioned into a square and a similar rectangle and this rectangle can then be split in the same way. After continuing this process for an arbitrary number of ...
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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.
Three interlocking golden rectangles inscribed in a convex regular icosahedron The convex regular icosahedron is usually referred to simply as the regular icosahedron , one of the five regular Platonic solids , and is represented by its Schläfli symbol {3, 5}, containing 20 triangular faces, with 5 faces meeting around each vertex.
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