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Silver Ratio

The quantity defined by the Continued Fraction

\begin{displaymath}
\delta_S \equiv [2,2,2,\ldots]=2+{1\over 2+{\strut\displayst...
... 2+{\strut\displaystyle 1\over\strut\displaystyle 2+\cdots}}}.
\end{displaymath}

It follows that

\begin{displaymath}
(\delta_S-1)^2 = 2,
\end{displaymath}

so

\begin{displaymath}
\delta_S = \sqrt{2}+1=2.41421\ldots.
\end{displaymath}

See also Golden Ratio, Golden Ratio Conjugate




© 1996-9 Eric W. Weisstein
1999-05-26