Metallic mean
id:
metallic-mean-184-23858
title:
Metallic mean
text:
The metallic mean of a natural number n is a positive real number, denoted here S n, that satisfies the following equivalent characterizations:
- the unique positive real number x such that x = n + 1 x
- the positive root of the quadratic equation x 2 − n x − 1 = 0
- the number n + n 2 + 4 2
- the number whose expression as a continued fraction is
- [ n ; n, n, n, n, … ] = n + 1 n + 1 n + 1 n + 1 n + ⋱ Metallic means are generalizations of the golden ratio and silver ratio, and share
brand slug:
wiki
category slug:
encyclopedia
description:
Generalization of golden and silver ratios
original url:
https://en.wikipedia.org/wiki/Metallic_mean
date created:
2014-10-14T10:18:09Z
date modified:
2024-09-07T00:47:23Z
main entity:
{"identifier":"Q11634820","url":"https://www.wikidata.org/entity/Q11634820"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/9/93/Fibonacci_spiral_34.svg","width":915,"height":579}
fields total:
13
integrity:
16