The quantity
![\begin{displaymath}
\phi_C \equiv {1\over\phi} = \phi-1={\sqrt{5}-1 \over 2} \approx 0.6180339887,
\end{displaymath}](g_1629.gif) |
(1) |
where
is the Golden Ratio. The golden ratio conjugate is sometimes also called the Silver Ratio.
A quantity similar to the Feigenbaum Constant can be found for the
th Continued Fraction representation
![\begin{displaymath}[a_0, a_1, a_2, \ldots].
\end{displaymath}](g_1630.gif) |
(2) |
Taking the limit of
![\begin{displaymath}
\delta_n\equiv {\sigma_n-\sigma_{n-1}\over \sigma_n-\sigma_{n+1}}
\end{displaymath}](g_1631.gif) |
(3) |
gives
![\begin{displaymath}
\delta\equiv \lim_{n\to\infty} = 1+\phi = 2+\phi_C.
\end{displaymath}](g_1632.gif) |
(4) |
See also Golden Ratio, Silver Ratio
© 1996-9 Eric W. Weisstein
1999-05-25