silver ratio

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


which suggests that the Pell numbersMathworldPlanetmath Pn can be used as convergentsMathworldPlanetmathPlanetmath. Similarly, the nth power of the silver ratio for n>0 is PnδS+Pn-1.

Title silver ratio
Canonical name SilverRatio
Date of creation 2013-03-22 16:42:10
Last modified on 2013-03-22 16:42:10
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Definition
Classification msc 40A05