Rational Numbers and Metallic Ratios

Authors

  • J. Suganthi Department of Mathematics, S.S.K.V. College of Arts and Science for Women, Kanchipuram, India
  • R. Sivaraman Department of Mathematics, Dwaraka Doss Goverdhan Doss Vaishnav College, Chennai, India https://orcid.org/0000-0001-5989-4422

DOI:

https://doi.org/10.37256/cm.5320243152

Keywords:

golden ratio, metallic ratio, linear combination, roots, cubic polynomial

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.

References

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Published

2024-09-05

Issue

Contemporary Mathematics, Volume 5 Issue 3 (2024), 2593-4131

Section

Research Article

License

Copyright (c) 2024 R. Sivaraman, et al

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

1.
Rational Numbers and Metallic Ratios. Contemp. Math. [Internet]. 2024 Sep. 5 [cited 2025 Dec. 24];5(3):3670-5. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/3152