Golden ratio and self-similarity in swimming: breast-stroke and the back-stroke

• Published in: Frontiers in human neuroscience Vol. 17; p. 1176866
• Main Authors: Verrelli, Cristiano M., Romagnoli, Cristian, Colistra, Nicolò, Ferretti, Ivo, Annino, Giuseppe, Bonaiuto, Vincenzo, Manzi, Vincenzo
• Format: Journal Article
• Language: English
• Published: Switzerland Frontiers Media S.A 24.07.2023
• Subjects: Fibonacci sequence; golden ratio; Human Neuroscience; neuroscience; self-similarity; swimming; swimming; golden ratio; self-similarity; Fibonacci sequence; neuroscience
• ISSN: 1662-5161; 1662-5161
• DOI: 10.3389/fnhum.2023.1176866

Dynamics-on-graph concepts and generalized finite-length Fibonacci sequences have been used to characterize, from a temporal point of view, both human walking & running at a comfortable speed and front-crawl & butterfly swimming strokes at a middle/long distance pace. Such sequences, in which the golden ratio plays a crucial role to describe self-similar patterns, have been found to be subtly experimentally exhibited by healthy (but not pathological) walking subjects and elite swimmers, in terms of durations of gait/stroke-subphases with a clear physical meaning. Corresponding quantitative indices have been able to unveil the resulting hidden time-harmonic and self-similar structures. In this study, we meaningfully extend such latest findings to the remaining two swimming strokes, namely, the breast-stroke and the back-stroke: breast-stroke, just like butterfly swimming, is highly technical and involves the complex coordination of the arm and leg actions, while back-stroke is definitely similar to front-crawl swimming. An experimental validation with reference to international-level swimmers is included.