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June 14, 20260 citationsOpen Access

Decimal-Metallic Ratios: A Comprehensive Family of Quadratic Irrationals unifying Classical Metallic Means, Deca-Metallic Ratios, and Primitive Pythagorean Triples

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CRChetansing Rajput

Key Points

  • The aim is to present a unified framework for understanding Decimal-Metallic Ratios and their relationships with classical means and Pythagorean triples.
  • Developed an infinite parametric family of quadratic irrationals
  • Demonstrated connections between classical metallic means and primitive Pythagorean triples
  • Utilized algebraic, geometric, and hyperbolic approaches to analyze the families
  • Establishes a coherent framework that relates Decimal-Metallic Ratios to existing mathematical theories
  • Shows potential applications in various areas of mathematics
  • Offers new insights into the structure of quadratic irrationals

Abstract

This paper introduces the Decimal-Metallic Ratios, a comprehensive infinite parametric family of quadratic irrationals that unifies the classical Metallic Means, the Deca-Metallic Ratios, and primitive Pythagorean triples within a single coherent algebraic, geometric, and hyperbolic framework.

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Cite This Study

Chetansing Rajput (2026) studied this question.

synapsesocial.com/papers/6a2e4779b1cc60ccdea8c05ehttps://doi.org/10.5281/zenodo.20651595
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