The Family of Metallic Means

Vera W. de Spinadel

Let me introduce you to the Metallic Means Family (MMF). Their members have, among other common characteristics, the property of carrying the name of a metal. Like the very well known Golden Mean and its relatives, the Silver Mean, the Bronze Mean, the Copper Mean, the Nickel Mean and many others. The Golden Mean has been used in a very big number of ancient cultures as a proportion basis to compose music, devise sculptures and paintings or construct temples and palaces (see Reference [1]). Some of the relatives of the Golden Mean have been used by physicists in their latest researches trying to analyze the behavior of non-linear dynamical systems in going from periodicity to quasi-periodicity ([2] and [3]). But in quite a different context, Jay Kappraff [4] uses the Silver Mean to describe and explain the roman system of proportions, referring to a mathematical property that, as we shall prove, it is common to all the members of this remarkable family.