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

Chetansing Rajput

doi:10.24297/jam.v20i.9088

Authors

Chetansing Rajput M.B.B.S. Nair Hospital (Mumbai University) India, Asst. Commissioner (Govt. of Maharashtra)

DOI:

https://doi.org/10.24297/jam.v20i.9088

Keywords:

Metallic Ratio, Pythagorean Triangles, Pascal’s Triangle, Golden Ratio, Pythagorean Triples, Metallic Ratio Triads, Right Triangle, Pythagoras Theorem, Metallic Mean

Abstract

The Primitive Pythagorean Triples are found to be the purest expressions of various Metallic Ratios. Each Metallic Mean is epitomized by one particular Pythagorean Triangle. Also, the Right Angled Triangles are found to be more “Metallic” than the Pentagons, Octagons or any other (n²+4)gons. The Primitive Pythagorean Triples, not the regular polygons, are the prototypical forms of all Metallic Means.

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References

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