Definitions for golden ratio

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Wiktionary

  1. golden ratio(Noun)

    The irrational number (approximately 1u00B7618), usually denoted by the Greek letter u03C6 (phi), which is equal the sum of its own reciprocal and 1, or, equivalently, is such that the ratio of 1 to the number is equal to the ratio of its reciprocal to 1.

Freebase

  1. Golden ratio

    In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The figure on the right illustrates the geometric relationship. Expressed algebraically: where the Greek letter phi represents the golden ratio. Its value is: The golden ratio is also called the golden section or golden mean. Other names include extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, and golden number. Many 20th century artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which can be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data.

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"golden ratio." Definitions.net. STANDS4 LLC, 2014. Web. 28 Jul 2014. <http://www.definitions.net/definition/golden ratio>.

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