# Category: Golden ratio

Penrose tiling
A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and aperiodic means that shifting any tiling with these sh
Golden-section search
The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal function with an extremum inside the interval,
William Schooling
Sir William Schooling KBE FRAS FSS (16 December 1860 – 18 February 1936) was a British expert on insurance and statistics. He was named a CBE in the 1918 Birthday Honours and a KBE in 1920 for his wor
833 cents scale
The 833 cents scale is a musical tuning and scale proposed by Heinz Bohlen based on combination tones, an interval of 833.09 cents, and, coincidentally, the Fibonacci sequence. The golden ratio is , w
Mark Barr
James Mark McGinnis Barr (May 18, 1871 – December 15, 1950) was an electrical engineer, physicist, inventor, and polymath known for proposing the standard notation for the golden ratio. Born in Americ
Lute of Pythagoras
The lute of Pythagoras is a self-similar geometric figure made from a sequence of pentagrams.
Rhombic triacontahedron
In geometry, the rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges an
Golden rectangle
In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, , which is (the Greek letter phi), where is approximately 1.618. Golden rectangles exhibit a special form of
Supergolden ratio
In mathematics, two quantities are in the supergolden ratio if the quotient of the larger number divided by the smaller one is equal to which is the only real solution to the equation . It can also be
Golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , wher
Bilinski dodecahedron
In geometry, the Bilinski dodecahedron is a convex polyhedron with twelve congruent golden rhombus faces. It has the same topology but a different geometry than the face-transitive rhombic dodecahedro
Coxeter's loxodromic sequence of tangent circles
In geometry, Coxeter's loxodromic sequence of tangent circles is an infinite sequence of circles arranged so that any four consecutive circles in the sequence are pairwise mutually tangent. This means
List of works designed with the golden ratio
Many works of art are claimed to have been designed using the golden ratio.However, many of these claims are disputed, or refuted by measurement. The golden ratio, an irrational number, is approximate
Golomb sequence
In mathematics, the Golomb sequence, named after Solomon W. Golomb (but also called Silverman's sequence), is a monotonically increasing integer sequence where an is the number of times that n occurs
Golden triangle (mathematics)
A golden triangle, also called a sublime triangle, is an isosceles triangle in which the duplicated side is in the golden ratio to the base side:
Golden spiral
In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter tur
Rhombic dodecahedron
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. It is a Catalan solid, and the dual polyhedron of the cubocta
Golden angle
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 leng
Golden rhombus
In geometry, a golden rhombus is a rhombus whose diagonals are in the golden ratio: Equivalently, it is the Varignon parallelogram formed from the edge midpoints of a golden rectangle.Rhombi with this
Kepler triangle
A Kepler triangle is a special right triangle with edge lengths in geometric progression. The ratio of the progression is where is the golden ratio, and the progression can be written: , or approximat
Jay Hambidge
Jay Hambidge (1867–1924) was a Canadian-born American artist who formulated the theory of "dynamic symmetry", a system defining compositional rules, which was adopted by several notable American and C
Vitruvian Man
The Vitruvian Man (Italian: L'uomo vitruviano; [ˈlwɔːmo vitruˈvjaːno]) is a drawing by the Italian Renaissance artist and scientist Leonardo da Vinci, dated to c. 1490. Inspired by the writings by the
Pentagram
A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersectin
Golden ratio base
Golden ratio base is a non-integer positional numeral system that uses the golden ratio (the irrational number 1 + √5/2 ≈ 1.61803399 symbolized by the Greek letter φ) as its base. It is sometimes refe