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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
A root-phi rectangle divides into a pair of Kepler triangles (right triangles with edge lengths in geometric progression). The root-φ rectangle is a dynamic rectangle but not a root rectangle. Its diagonal equals φ times the length of the shorter side. If a root-φ rectangle is divided by a diagonal, the result is two congruent Kepler triangles.
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The following other wikis use this file: Usage on ca.wikipedia.org Constant matemàtica; Sòlid platònic; Usage on de.wikipedia.org Goldener Schnitt
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