John D. Cook • 8/4/2026

Ratio of metallic ratios

This article discusses metallic ratios, a generalization of the golden ratio, where the nth metallic ratio M(n) has a continued fraction of all n's. It explains that for large n, M(n) ≈ n, allowing any positive real number to be approximated by a ratio of metallic ratios. The author provides Python code to find metallic ratio ratios that approximate π within 0.001, finding M(132)/M(42) ≈ 3.1412, and proves no smaller pair works. The post is technical, involving mathematical concepts and programming, relevant to IT/TECHNOLOGY.

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#Python #number theory #Approximation