KnowraGolden ratioLinked fromLinked fromThe 18 pages that link to Golden ratio, each with the reason it gives.All 18Broader topic 5Related 10Compared with 3Composition (visual arts)Compared with: It is often proposed as a compositional rule, unlike flexible arrangements based on visual judgment.Irrational numberBroader topic: Its formula makes its irrationality follow from that of √5.Continued fractionBroader topic: Its continued fraction [1; 1, 1, …] has the slowest-converging simple continued-fraction pattern.Fibonacci sequenceRelated: Ratios of consecutive Fibonacci numbers approach this number.Isosceles triangleRelated: The golden triangle's equal sides and base connect its geometry to this proportion.RatioBroader topic: It is a named constant arising from a specific proportion between two lengths.ProportionBroader topic: It is a specific numerical proportion often proposed as an ideal relationship between parts.Euler's NumberCompared with: It is another famous mathematical constant, defined by a different characteristic relation.Constructible numberRelated: It is constructible as a root of a quadratic equation and appears in the regular pentagon.Nicolas PoussinCompared with: Claims that Poussin systematically built compositions around this ratio are disputed, unlike his evident use of ordered design.Dirichlet's approximation theoremRelated: Its continued fraction makes it a limiting example for how well irrationals can be approximated.Lucas sequenceRelated: Its powers appear in closed forms for Fibonacci numbers and classical Lucas numbers.Regular dodecahedronRelated: Pentagonal proportions make the golden ratio appear in the dodecahedron’s coordinates and diagonals.Square root of 2Related: Like square root of 2, it is irrational, but its continued fraction has a different repeating pattern.Mathematical constantBroader topic: The golden ratio is a named constant arising from a simple proportion.Mathematics and artRelated: Artists and designers have invoked it as a compositional proportion, though claims about its use require care.Regular icosahedronRelated: The coordinates of a regular icosahedron involve golden-ratio proportions.DecagonRelated: The golden ratio appears in the side and diagonal relationships of a regular decagon inscribed in a circle.
KnowraGolden ratioLinked fromLinked fromThe 18 pages that link to Golden ratio, each with the reason it gives.All 18Broader topic 5Related 10Compared with 3Composition (visual arts)Compared with: It is often proposed as a compositional rule, unlike flexible arrangements based on visual judgment.Irrational numberBroader topic: Its formula makes its irrationality follow from that of √5.Continued fractionBroader topic: Its continued fraction [1; 1, 1, …] has the slowest-converging simple continued-fraction pattern.Fibonacci sequenceRelated: Ratios of consecutive Fibonacci numbers approach this number.Isosceles triangleRelated: The golden triangle's equal sides and base connect its geometry to this proportion.RatioBroader topic: It is a named constant arising from a specific proportion between two lengths.ProportionBroader topic: It is a specific numerical proportion often proposed as an ideal relationship between parts.Euler's NumberCompared with: It is another famous mathematical constant, defined by a different characteristic relation.Constructible numberRelated: It is constructible as a root of a quadratic equation and appears in the regular pentagon.Nicolas PoussinCompared with: Claims that Poussin systematically built compositions around this ratio are disputed, unlike his evident use of ordered design.Dirichlet's approximation theoremRelated: Its continued fraction makes it a limiting example for how well irrationals can be approximated.Lucas sequenceRelated: Its powers appear in closed forms for Fibonacci numbers and classical Lucas numbers.Regular dodecahedronRelated: Pentagonal proportions make the golden ratio appear in the dodecahedron’s coordinates and diagonals.Square root of 2Related: Like square root of 2, it is irrational, but its continued fraction has a different repeating pattern.Mathematical constantBroader topic: The golden ratio is a named constant arising from a simple proportion.Mathematics and artRelated: Artists and designers have invoked it as a compositional proportion, though claims about its use require care.Regular icosahedronRelated: The coordinates of a regular icosahedron involve golden-ratio proportions.DecagonRelated: The golden ratio appears in the side and diagonal relationships of a regular decagon inscribed in a circle.