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Preserved in Portico This version is not peer-reviewed
Metallic Ratios are Uniquely Defined by an Acute Angle of a Right Triangle
Version 1
: Received: 5 January 2024 / Approved: 5 January 2024 / Online: 8 January 2024 (06:20:05 CET)
Version 2 : Received: 9 January 2024 / Approved: 10 January 2024 / Online: 10 January 2024 (04:28:16 CET)
Version 3 : Received: 15 January 2024 / Approved: 16 January 2024 / Online: 16 January 2024 (06:19:33 CET)
Version 4 : Received: 1 February 2024 / Approved: 1 February 2024 / Online: 2 February 2024 (04:33:46 CET)
Version 2 : Received: 9 January 2024 / Approved: 10 January 2024 / Online: 10 January 2024 (04:28:16 CET)
Version 3 : Received: 15 January 2024 / Approved: 16 January 2024 / Online: 16 January 2024 (06:19:33 CET)
Version 4 : Received: 1 February 2024 / Approved: 1 February 2024 / Online: 2 February 2024 (04:33:46 CET)
A peer-reviewed article of this Preprint also exists.
Łukaszyk, S. (2024). Metallic Ratios and Angles of a Real Argument. IPI Letters, 2(1), 26–33. https://doi.org/10.59973/ipil.55 Łukaszyk, S. (2024). Metallic Ratios and Angles of a Real Argument. IPI Letters, 2(1), 26–33. https://doi.org/10.59973/ipil.55
Abstract
We show that metallic ratios for real k are uniquely defined by an acute angle of a right triangle, where for k ≠ {0, ±2} this angle is a logarithm of a normalized complex number, and for rational k this number is defined by a Pythagorean triple.
Keywords
metallic ratios; Pythagorean triples; emergent dimensionality
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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