Metallic Ratios and Angles of a Real Argument


  • Szymon Łukaszyk Lukaszyk Patent Attorneys, G lowackiego 8, 40-052 Katowice, Poland



Metallic ratios; , Metallic ratios;, Metallic angles; , Pythagorean triples;, Emergent dimensionality; , Mathematical physics


We extend the concept of metallic ratios to the real argument n considered as a dimension by analytic continuation showing that they are defined by an argument of a normalized complex number, and for rational n ≠ {0, ±2}, they are defined by Pythagorean triples. We further extend the concept of metallic ratios to metallic angles.


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2024-02-23 — Updated on 2024-03-28


How to Cite

Łukaszyk, S. (2024). Metallic Ratios and Angles of a Real Argument. IPI Letters, 2(1), 26–33. (Original work published February 23, 2024)




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