# 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

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

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 |
---|---|

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 |