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The golden ratio φ and its negative reciprocal −φ −1 are the two roots of the quadratic polynomial x 2 − x − 1. The golden ratio's negative −φ and reciprocal φ −1 are the two roots of the quadratic polynomial x 2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer.
Golden spirals are self-similar. The shape is infinitely repeated when magnified. In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. [1] That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.
Other scholars question whether the golden ratio was known to or used by Greek artists and architects as a principle of aesthetic proportion. [11] Building the Acropolis is calculated to have been started around 600 BC, but the works said to exhibit the golden ratio proportions were created from 468 BC to 430 BC.
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Golden ratio, a specific mathematical ratio (sometimes called golden mean) Golden ratio (mathematics and visual art) The Golden Mean (1993), third novel in The Griffin and Sabine Trilogy by Nick Bantock; The golden-mean fallacy, another name for the argument to moderation; Doctrine of the Golden Mean, a chapter in Li Ji, one of the Four Books ...
Adolf Zeising (24 September 1810 – 27 April 1876) was a German psychologist, whose main interests were mathematics and philosophy.. Among his theories, Zeising claimed to have found the golden ratio expressed in the arrangement of branches along the stems of plants and of veins in leaves.
James Mark McGinnis Barr [1] (18 May 1871 – 15 December 1950) [2] [3] [4] was an electrical engineer, physicist, inventor, and polymath known for proposing the standard notation for the golden ratio. Born in America, but with English citizenship, Barr lived in both London and New York City at different times of his life.
The rediscovery of Dee and Kelley's material by Samuel Liddell MacGregor Mathers of the Hermetic Order of the Golden Dawn in the 1880s led to Mathers developing the material into a comprehensive system of ceremonial magic. Magicians invoked the Enochian deities whose names were written on the tablets.