Related Experiment Video
Updated: Jul 19, 2025

Cardiac Muscle Cell-based Actuator and Self-stabilizing Biorobot - Part 2
Published on: May 9, 2017
Golden ratio and self-similarity in swimming: breast-stroke and the back-stroke
Cristiano M Verrelli1, Cristian Romagnoli2,3, Nicolò Colistra1
1Department of Electronic Engineering, University of Rome Tor Vergata, Rome, Italy.
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.
Related Concept Videos
Modeling and Similitude
Typical Model Studies
Design Example: Creating a Hydraulic Model of a Dam Spillway
Hydrostatic Pressure Force on a Curved Surface

