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The Golden Ratio in Nature: A Tour across Length Scales

Marples, Callum Robert; Williams, Philip Michael


Callum Robert Marples


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 is claimed to appear; beginning at astronomical scales and progressing to smaller lengths, until reaching those of atomic and quantum physics. For each phenomenon discussed, the evidence for the presence of the Golden ratio is assessed. In making such a tour across length scales, it is illustrated just how prevalent this single number is within the natural universe.


Marples, C. R., & Williams, P. M. (2022). The Golden Ratio in Nature: A Tour across Length Scales. Symmetry, 14(10), Article 2059.

Journal Article Type Article
Acceptance Date Sep 23, 2022
Online Publication Date Oct 3, 2022
Publication Date Oct 1, 2022
Deposit Date Oct 5, 2022
Publicly Available Date Oct 14, 2022
Journal Symmetry
Electronic ISSN 2073-8994
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 14
Issue 10
Article Number 2059
Keywords Physics and Astronomy (miscellaneous); General Mathematics; Chemistry (miscellaneous); Computer Science (miscellaneous)
Public URL
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