Article
Version 1
Preserved in Portico This version is not peer-reviewed
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.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment