Golden Ratio, Silver Ratio and other Metallic Means ; Geometric Substantiation of all Metallic Ratios
DOI:
https://doi.org/10.24297/jam.v20i.9034Keywords:
Metallic Mean, Metallic Ratio, Golden Proportion, Lucas Numbers, Pell Numbers, Right Triangle, Golden Mean, Silver Ratio, Divine Proportion, Pythagoras Theorem, Phi, Pi, Fibonacci sequence, Golden RatioAbstract
This paper introduces the concept of special right angled triangles those epitomize the different Metallic Ratios. These right triangles not only have the precise Metallic Means embedded in all their geometric features, but they also provide the most accurate geometric substantiation of all Metallic Means. These special right triangles manifest the corresponding Metallic Ratios more holistically than the regular pentagon, octagon or tridecagon, etc
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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 : Beyond the Golden Ratio: The Geometric Substantiation of all Metallic Ratios. JOURNAL OF ADVANCES IN MATHEMATICS. 20. 19-42.
https://doi.org/10.24297/jam.v20i.8945
Sloane, N. J. A. Sequences A000045/M0692, A000204/M2341 in "The On-Line Encyclopedia of Integer Sequences."
https://oeis.org/A000045 & https://oeis.org/A000204
Sloane, N. J. A. Sequences A000129/M1413, A002203/M0360, in "The On-Line Encyclopedia of Integer Sequences."
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Copyright (c) 2021 Chetansing Rajput
This work is licensed under a Creative Commons Attribution 4.0 International License.
All articles published in Journal of Advances in Linguistics are licensed under a Creative Commons Attribution 4.0 International License.
