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Homesilver ratio

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# silver ratio

The silver ratio is the sum of 1 and the square root of 2, represented by the Greek letter delta with a subscript S. That is, $\delta_{S}=1+\sqrt{2}$, with an approximate value of 2.4142135623730950488 (see A014176 in Sloane’s OEIS). Its continued fraction is

$2+\frac{1}{2+\frac{1}{2+\frac{1}{2+\ddots}}},$ |

which suggests that the Pell numbers $P_{n}$ can be used as convergents. Similarly, the $n$th power of the silver ratio for $n>0$ is $P_{n}\delta_{S}+P_{{n-1}}$.

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Reference

## Mathematics Subject Classification

40A05*no label found*

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## Comments

## Might be interesting to point out comparison with Golden Rat...

(If there is one...)

Are there also aluminum, platinum ratios?

## Re: Might be interesting to point out comparison with Golden...

There might be. I'll Google for them, see if I come up with anything.