Phi -Bonacci Butterfly Stroke Numbers to Assess Self-Similarity in Elite Swimmers

Cristiano Maria Verrelli, Cristian Romagnoli, Roxanne Jackson, Ivo Ferretti, Giuseppe Annino and Vincenzo Bonaiuto
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Cristiano Maria Verrelli: Department of the Electronic Engineering, University of Rome Tor Vergata, via del Politecnico 1, 00133 Rome, Italy
Cristian Romagnoli: Department for Life Quality Studies, University of Bologna, 47900 Rimini, Italy
Roxanne Jackson: Institute of Automation Technology, Otto-von-Guericke University Magdeburg, 39106 Magdeburg, Germany
Ivo Ferretti: Biomechanical and Video-Analysis Area for the National Teams of Federazione Italiana Nuoto (FIN), 00100 Rome, Italy
Giuseppe Annino: Sport Engineering Lab, Department of Industrial Engineering, University of Rome Tor Vergata, 00133 Rome, Italy
Vincenzo Bonaiuto: Sport Engineering Lab, Department of Industrial Engineering, University of Rome Tor Vergata, 00133 Rome, Italy

Mathematics, 2021, vol. 9, issue 13, 1-12

Abstract: A harmonically self-similar temporal partition, which turns out to be subtly exhibited by elite swimmers at middle distance pace, is formally defined for one of the most technically advanced swimming strokes—the butterfly. This partition relies on the generalized Fibonacci sequence and the golden ratio. Quantitative indices, named ? -bonacci butterfly stroke numbers, are proposed to assess such an aforementioned hidden time-harmonic and self-similar structure. An experimental validation on seven international-level swimmers and two national-level swimmers was included. The results of this paper accordingly extend the previous findings in the literature regarding human walking and running at a comfortable speed and front crawl swimming strokes at a middle/long distance pace.

Keywords: generalized Fibonacci sequence; self-similarity; golden ratio; butterfly swimming; elite swimmers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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