Metallic Ratios : The Mathematical Relationships between different Metallic Means

Chetansing Rajput

doi:10.24297/jam.v20i.9023

Metallic Ratios : The Mathematical Relationships between different Metallic Means

Authors

Chetansing Rajput Dr. , ACST

DOI:

https://doi.org/10.24297/jam.v20i.9023

Keywords:

Metallic Ratio, Golden Proportion, Lucas Numbers, Pell Numbers, Right Triangle, Golden Mean, Silver Ratio, Divine Proportion, Pythagoras Theorem, Phi, Pi, Fibonacci sequence, Golden Ratio, Metallic Mean

Abstract

This paper introduces the precise mathematical relationships between different Metallic Ratios. Certain distinctive mathematical correlations are found to exist between various Metallic Means. This work presents the empirical formulae those provide the exact mathematical relationships between different Metallic Ratios.

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References

Rajput, Chetansing. (2021). Golden Ratio. JOURNAL OF ADVANCES IN MATHEMATICS. 20. 19-42. https://doi.org/10.24297/jam.v20i.8945

Rajput, Chetansing. (2021). Metallic Means and Right Triangles: The Geometric Substantiation of all Metallic Ratios. JOURNAL OF ADVANCES IN MATHEMATICS. 20. 167-173. https://doi.org/10.24297/jam.v20i.9029 and https://doi.org/10.24297/jam.v20i.9034

Sloane, N. J. A. Sequences A000045/M0692, A000204/M2341 in "The On-Line Encyclopedia of Integer Sequences." https://oeis.org/A000045 and https://oeis.org/A000204

Sloane, N. J. A. Sequences A000129/M1413, A002203/M0360, in "The On-Line Encyclopedia of Integer Sequences." http://oeis.org/A000129 and http://oeis.org/A002203

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Published

2021-05-23

How to Cite

Rajput, C. (2021). Metallic Ratios : The Mathematical Relationships between different Metallic Means. JOURNAL OF ADVANCES IN MATHEMATICS, 20, 158–166. https://doi.org/10.24297/jam.v20i.9023