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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.
Diagram showing the golden ratio for zettai ryōiki. The ideal zettai ryōiki ratio for the length of the miniskirt, the exposed portion of thigh, and the over-knee part of the socks is 4:1:2.5, with a tolerance of 25%. [3] [4] [5] The ratio has also been referred to as a golden ratio (黄金比, ōgonhi) among fans. [6]
Divina proportione (15th century Italian for Divine proportion), later also called De divina proportione (converting the Italian title into a Latin one) is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, completed by February 9th, 1498 [1] in Milan and first printed in 1509. [2]
the ratio of hip circumference to shoulder circumference varies by biological sex: the average ratio for women is 1:1.03, for men it is 1:1.18. [9] legs (floor to crotch, which are typically three-and-a-half to four heads long; arms about three heads long; hands are as long as the face. [10]
The golden angle is the angle subtended by the smaller (red) arc when two arcs that make up a circle are in the golden ratio. In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio; that is, into two arcs such that the ratio of the length of the smaller arc to the length of the larger arc is the same as ...
Georges Seurat, 1887-88, Parade de cirque (Circus Sideshow) with a 4 : 6 ratio division and golden mean overlay, showing only a close approximation to the divine proportion. Matila Ghyka [30] and others [31] contend that Georges Seurat used golden ratio proportions in paintings like Parade de cirque, Le Pont de Courbevoie, and Bathers at ...
A golden triangle. The ratio a/b is the golden ratio φ. The vertex angle is =.Base angles are 72° each. Golden gnomon, having side lengths 1, 1, and .. A golden triangle, also called a sublime triangle, [1] is an isosceles triangle in which the duplicated side is in the golden ratio to the base side:
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.