Metallic Ratios, Pythagorean Triples & p≡1(mod 4) Primes : Metallic Means, Right Triangles and the Pythagoras Theorem

Chetansing Rajput

doi:10.24297/jam.v20i.9075

Authors

Chetansing Rajput Dr. , ACST

DOI:

https://doi.org/10.24297/jam.v20i.9075

Keywords:

Metallic Ratio, Pascal’s Triangle, Golden Ratio, Bronze Ratio, Pythagorean Triples, 3 6 9, Metallic Ratio Triads, Metallic Numbers, Right Triangle, Silver Ratio, Phi, Pi, Lucas, Pell, Fibonacci, Pythagoras Theorem, Metallic Mean

Abstract

This paper synergizes the newly discovered geometry of all Metallic Means and the recently published mathematical formulae those provide the precise correlations between different Metallic Ratios. The paper illustrates the concept of the “Triads of Metallic Means”, and aslo the close correspondence between Metallic Ratios and the Pythagorean Triples as well as Pythagorean Primes.

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References

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Rajput, Chetansing (2021). Metallic Ratios and the Digits 3 6 9, Mathematical Relations between different Metallic Means, And the Special Significance of Digits 3, 6, 9 in the realm of Metallic Numbers. JOURNAL OF ADVANCES IN MATHEMATICS, 20, 167-173. https://doi.org/10.24297/jam.v20i.9029