Rational Numbers and Metallic Ratios

Abstract

Metallic ratios are class of real numbers which are positive roots of specific quadratic equation. In this paper, we had proved results regarding expressing any integer as well as rational numbers in terms of metallic ratios in the form of a cubic polynomial with integer coefficients. Three theorems had been established to meet this objective. This novel idea adds one more dimension to existing known properties of metallic ratios. Detailed explanation is provided in the final section to verify the results obtained.