Metallic mean

Common card · No. 492012

The metallic mean (also metallic ratio, metallic constant, or noble mean) of a natural number n is a positive real number, denoted here S n , {\displaystyle S_{n},} that satisfies the following equivalent characterizations: the unique positive real number x {\displaystyle x} such that x = n + 1 x {\textstyle x=n+{\frac {1}{x}}} the positive root of the quadratic equation x 2 − n x − 1 = 0 {\displaystyle x^{2}-nx-1=0} the number n +...

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