ArticleFrontiers in human neuroscience2023
Golden ratio and self-similarity in swimming: breast-stroke and the back-stroke.
Article in Frontiers in human neuroscience, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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Who cites it
5 citing papers in PubMed.
- The relationship between stroke length, stroke frequency, glide time and performance in swimmers: a biomechanical study.BMC sports science, medicine & rehabilitation · 2026Article
- Wearable Sensor-Based Gait Analysis in Benign Paroxysmal Positional Vertigo: Quantitative Assessment of Residual Dizziness Using the φ-Bonacci Framework.Life (Basel, Switzerland) · 2026Article
- Nonlinear interaction between stroke length and stroke rate in elite swimming.Frontiers in sports and active living · 2026Article
- Hidden time-patterns in cyclic human movements: a matter of temporal Fibonacci sequence generation and harmonization.Frontiers in human neuroscience · 2025Article
- Editorial: Assessment and monitoring of human movement.Frontiers in physiology · 2025Article
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Authors and funding
7 authors.
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Abstract
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.
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