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)
|
| 👁 Image | 👁 = | 👁 phi-1 |
(3)
|
| 👁 Image | 👁 = | 👁 2/(1+sqrt(5)) |
(4)
|
| 👁 Image | 👁 = | 👁 (sqrt(5)-1)/2 |
(5)
|
| 👁 Image | 👁 = | 👁 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 RatioExplore with Wolfram|Alpha
More things to try:
References
👁 Update a link
Knott, 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 ConjugateCite this as:
Weisstein, Eric W. "Golden Ratio Conjugate." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GoldenRatioConjugate.html