# 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 $P_{n}\delta_{S}+P_{n-1}$.

Title silver ratio SilverRatio 2013-03-22 16:42:10 2013-03-22 16:42:10 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Definition msc 40A05