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

Front Hum Neurosci. 2023 Jul 24;17:1176866. doi: 10.3389/fnhum.2023.1176866. eCollection 2023.


Introduction: 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.

Results: 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.

Keywords: Fibonacci sequence; golden ratio; neuroscience; self-similarity; swimming.

Grants and funding

Pegaso Open University contributed to the publication fees, for most of them.