Article
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The Golden Ratio in Nature: A Tour Across Length Scales
Version 1
: Received: 15 August 2022 / Approved: 16 August 2022 / Online: 16 August 2022 (14:29:27 CEST)
A peer-reviewed article of this Preprint also exists.
Marples, C.R.; Williams, P.M. The Golden Ratio in Nature: A Tour Across Length Scales. Symmetry 2022, 14, 2059. Marples, C.R.; Williams, P.M. The Golden Ratio in Nature: A Tour Across Length Scales. Symmetry 2022, 14, 2059.
Abstract
The Golden ratio is an irrational number that has a tendency to appear in many different scientific and artistic fields. It may be found in natural phenomena across a vast range of length scales; from galactic to atomic. In this review, the mathematical properties of the Golden ratio are discussed before exploring where in nature it has been found; beginning at astronomical scales and progressing to smaller lengths, until reaching those of atomic and quantum physics. In making such a tour across length scales, it is illustrated just how prevalent this single number is within the natural universe.
Keywords
Golden ratio; Irrational numbers; Fibonacci sequence; Spiral galaxy; Planetary orbits; KAM Theorem; Ultimatum game; Proteins; Penrose tiling; Quasicrystals
Subject
Physical Sciences, Atomic and Molecular Physics
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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