Metallic Means in Primitive Pythagorean Triples : Metallic Ratios substantiated in Pythagorean Triangles  and other Right Angled Triangles

Chetansing Rajput

doi:10.24297/jam.v24i.9832

Authors

Chetansing Rajput Dr.

DOI:

https://doi.org/10.24297/jam.v24i.9832

Keywords:

metallic ratios, Metallic Means, Pythagorean Triples, Right Triangles

Abstract

This paper elaborates the precise correlation between metallic ratios and the different families of primitive Pythagorean triples. This paper also discusses the explicit formulae those provide the mathematical relationships between different metallic numbers. Main purpose of this paper is to highlight the geometric substantiation of metallic means in Pythagorean triples and other right triangles, and the trigonometric expression of the metallic ratios.

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References

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Chetansing Rajput (2021). Metallic ratios in primitive Pythagorean triples: Metallic means embedded in Pythagorean triangles and other right triangles. Metallic Ratios in Primitive Pythagorean Triples : Metallic Means embedded in Pythagorean Triangles and other Right Triangles | JOURNAL OF ADVANCES IN MATHEMATICS Journal of Advances in Mathematics, 20, 312–344.

Rajput, Chetansing; Manjunath, Hariprasad (2024). "Metallic means and Pythagorean triples | Notes on Number Theory and Discrete Mathematics". Bulgarian Academy of Sciences.