Supergolden ratio

Supergolden ratio
	A supergolden rectangle contains three scaled copies of itself, ψ = ψ−1 + 2ψ−3 + ψ−5
Rationality	irrational algebraic
Symbol	ψ
Representations
Decimal	1.4655712318767680266567312...
Algebraic form	real 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 $x 3 = x 2 + 1.$

The name supergolden ratio results from analogy with the golden ratio, the positive solution of the equation $x 2 = x + 1.$

A triangle with side lengths $ψ, 1,$ and $1 ∕ ψ$ has an angle of exactly 120 degrees.^[1]

^ Sloane, N. J. A. (ed.). "Sequence A092526". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[1] Sloane, N. J. A. (ed.). "Sequence A092526". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

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