PlanetMath: silver ratio

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silver ratio

(Definition)

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

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

which suggests that the Pell numbers

can be used as convergents. Similarly, the

th power of the silver ratio for

is $P_n\delta_S + P_{n - 1}$ .

"silver ratio" is owned by PrimeFan.

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Attachments:: silver rectangle (Definition) by PrimeFan

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Cross-references: power, convergents, Pell numbers, continued fraction, OEIS, subscript, Greek letter, square root of 2, sum
There are 4 references to this entry.

This is version 2 of silver ratio, born on 2007-02-15, modified 2007-02-16.
Object id is 8917, canonical name is SilverRatio.
Accessed 809 times total.

Classification:

AMS MSC:

40A05 (Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Convergence and divergence of series and sequences)

Pending Errata and Addenda

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