Silver ratio

The silver ratio is a number one greater than the square root of two; that is,

$\delta _{S}={\sqrt {2}}+1\approx 2.414213562373095048801688724210\dots$

The silver ratio is also defined by the continued fraction [2; 2, 2, 2, ...]:

$\delta _{S}=2+{\frac {1}{2+{\frac {1}{2+{\frac {1}{2+\cdots }}}}}}$

Its name is an allusion to the more well-known golden ratio, by analogy with the noble metals -- copper, silver, and gold.

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It follows that :

$(\delta _{S}-1)^{2}=2$

The sequence , of power fractional parts, where is the fractional part, is equidistributed for almost all real numbers x > 1, with the silver ratio being one exception.

The golden ratio conjugate is also sometimes erroneously termed the silver ratio.