Cyclic Human Movements and Time-Harmonic Structures: Role of the Golden Ratio in the Tennis Forehand

Generalized Fibonacci sequences are Fibonacci sequences that start with positive integers—called seeds—other than 0 and 1. They have been very recently used to temporally characterize cyclic human movements such as walking, running, and swimming. Within such sequences, the golden ratio describes, in terms of durations of specific gait/stroke-subphases, self-similar patterns: they are experimentally exhibited not only by healthy walking subjects—harmonic proportions might be reduced or destroyed by disorders with neurological implications—but also by elite swimmers. Quantitative indices have been accordingly defined to unveil hidden self-similar & time-harmonic structures while providing an estimate of how much the larger-scale structure resembles the smaller-scale structure through the generation of a self-referential loop. In this paper, all such different scenarios are first reviewed from above and stitched together on a common logical platform, to provide the readers with a comprehensive view of the issue while allowing them to follow and define new research directions. One among them, involving the fascinating tennis framework, is successfully highlighted in detail.