Metallic Means : Beyond the Golden Ratio, New Mathematics and Geometry of all Metallic Ratios based upon Right Triangles, The Formation of the Triples of Metallic Means, And their Classical Correspondence with Pythagorean Triples and p≡1(mod 4) Primes, A
Keywords:Metallic Mean, Golden Ratio, Pythagorean Primes, Pythagorean Triples, 3 6 9, Metallic Triples, Metallic Ratio, Golden Proportion, Lucas Numbers, , Pell Numbers, Metallic Numbers, Right Triangle, Golden Mean, Silver Ratio, Divine Proportion, Pythagoras Theorem, Phi, Pi, Fibonacci sequence, Pell Numbers
This paper brings together the newly discovered generalised geometry of all Metallic Means and the recently published mathematical formulae those provide the precise correlations between different Metallic Ratios. The paper also puts forward the concept of the “Triples of Metallic Means”. This work also introduces the close correspondence between Metallic Ratios and the Pythagorean Triples as well as Pythagorean Primes. Moreover, this work illustrates the intriguing relationship between Metallic Numbers and the Digits 3 6 9.
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