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Supergolden Triangle

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SupergoldenTriangle

The reciprocal proportion triangle with edge lengths psi^(-1), 1, and psi where psi is the supergolden ratio may be termed the supergolden triangle. It has angles

alpha_1=cos^(-1)(1/(24)(-8+(8416-864sqrt(93))^(1/3)+2^(5/3)(263+27sqrt(93))^(1/3)))
(1)
alpha_2=cos^(-1)(1/(24)(-16+(5984-288sqrt(93))^(1/3)+2^(5/3)(187+9sqrt(93))^(1/3)))
(2)
alpha_3=(2pi)/3,
(3)

the largest of which is exactly 120 degrees.

See also

Reciprocal Proportion Triangle, Supergolden Ratio, Supergolden Rectangle

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Cite this as:

Weisstein, Eric W. "Supergolden Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SupergoldenTriangle.html