Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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)

How to cite: Marples, C.R.; Williams, P.M. The Golden Ratio in Nature: A Tour Across Length Scales. Preprints 2022, 2022080293 (doi: 10.20944/preprints202208.0293.v1). Marples, C.R.; Williams, P.M. The Golden Ratio in Nature: A Tour Across Length Scales. Preprints 2022, 2022080293 (doi: 10.20944/preprints202208.0293.v1).

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, Other

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