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Golden Ratio Conjugate


The defining equation for the golden ratio phi is

 x^2-x-1=0,
(1)

which has two real roots: the golden ratio phi=1.61803... and its conjugate -phi^(-1)=-0.61803.... The absolute value of -phi^(-1) therefore has the value

Phi=1/phi
(2)
=phi-1
(3)
=2/(1+sqrt(5))
(4)
=(sqrt(5)-1)/2
(5)
=0.6180339887...
(6)

(OEIS A094214).

Phi is sometimes also called the "silver ratio," though that term is more commonly applied to the constant delta_S=1+sqrt(2).


See also

Golden Ratio, Silver Ratio

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References

Update a linkKnott, R. "Fibonacci Numbers and the Golden Section." http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/Sloane, N. J. A. Sequence A094214 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Golden Ratio Conjugate

Cite this as:

Weisstein, Eric W. "Golden Ratio Conjugate." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GoldenRatioConjugate.html

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