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

Author:

Verrelli Cristiano M.,Romagnoli Cristian,Colistra Nicolò,Ferretti Ivo,Annino Giuseppe,Bonaiuto Vincenzo,Manzi Vincenzo

Abstract

IntroductionDynamics-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.ResultsIn 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.

Publisher

Frontiers Media SA

Subject

Behavioral Neuroscience,Biological Psychiatry,Psychiatry and Mental health,Neurology,Neuropsychology and Physiological Psychology

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