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Supergolden ratio information


Supergolden ratio
A supergolden rectangle contains three scaled copies of itself, ψ = ψ-1 + 2ψ-3 + ψ-5
Rationalityirrational algebraic
Symbolψ
Representations
Decimal1.4655712318767680266567312...
Algebraic formreal root of x3 = x2 + 1
Continued fraction (linear)[1;2,6,1,3,5,4,22,1,1,4,1,2,84,...]
not periodic
infinite

In mathematics, the supergolden ratio is a geometrical proportion close to 85/58. Its true value is the real solution of the equation x3 = x2 + 1.

The name supergolden ratio results from analogy with the golden ratio, the positive solution of the equation x2 = x + 1.

A triangle with side lengths ψ, 1, and ψ-1 has an angle of exactly 120 degrees opposite the side of length ψ.[1]
  1. ^ Sloane, N. J. A. (ed.). "Sequence A092526". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

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