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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.
The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio, φ, so that the acute angles on each face measure 2 arctan( 1 / φ ) = arctan(2), or approximately 63.43°. A rhombus so obtained is called a golden rhombus.
Three mutually perpendicular golden ratio rectangles, with edges connecting their corners, form a regular icosahedron. Another way to construct it is by putting two points on each surface of a cube. In each face, draw a segment line between the midpoints of two opposite edges and locate two points with the golden ratio distance from each midpoint.
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:
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 ...
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]
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It is a parallelohedron because it can be space-filling a honeycomb in which all of its copies meet face-to-face. [7] More generally, every parellelohedron is zonohedron, a centrally symmetric polyhedron with centrally symmetric faces. [8] As a parallelohedron, the rhombic dodecahedron can be constructed with four sets of six parallel edges. [7]