Preprint Communication Version 3 Preserved in Portico This version is not peer-reviewed

Metallic Ratios are Defined by an Argument of a Normalized Complex Number

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)

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 defined by an argument of a normalized complex number, while for rational k ≠ {0, ±2}, they are defined by Pythagorean triples. We further extend the concept of metallic ratios to metallic angles.

Keywords

metallic ratios; Pythagorean triples; emergent dimensionality; mathematical physics

Subject

Computer Science and Mathematics, Mathematics

Comments (1)

Comment 1
Received: 16 January 2024
Commenter: Szymon Łukaszyk
Commenter's Conflict of Interests: Author
Comment: 1. Introducing metallic angles and discussing their properties.
2. Improvements in reasoning and clarity.
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