Metallic mean

The metallic means (also ratios or constants) of the successive natural numbers are the continued fractions: The golden ratio (1.618...) is the metallic mean between 1 and 2, while the silver ratio (2.414...) is the metallic mean between 2 and 3. The term "bronze ratio" (3.303...), or terms using other names of metals (such as copper or nickel), are occasionally used to name subsequent metallic means. The values of the first ten metallic means are shown at right. Notice that each metallic mean is a root of the simple quadratic equation:, where is any positive natural number.

Metallic mean

The metallic means (also ratios or constants) of the successive natural numbers are the continued fractions: The golden ratio (1.618...) is the metallic mean between 1 and 2, while the silver ratio (2.414...) is the metallic mean between 2 and 3. The term "bronze ratio" (3.303...), or terms using other names of metals (such as copper or nickel), are occasionally used to name subsequent metallic means. The values of the first ten metallic means are shown at right. Notice that each metallic mean is a root of the simple quadratic equation:, where is any positive natural number.