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

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-12
DOI
https://doi.org/10.5281/zenodo.20651596
Primary Topic
Mathematics and Applications
Type
preprint
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preprint

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

Chetansing K. Rajput
Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
preprint

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

Chetansing K. Rajput
preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
DOIOpen Access PDFOpenAlex
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Decimal-Metallic Ratios: A Comprehensive Family of Quadratic Irrationals unifying Classical Metallic Means, Deca-Metallic Ratios, and Primitive Pythagorean Triples — Chetansing K. Rajput · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS