Human movements, such as walking and running, are able to generate rhythmic motor patterns, with the consequent appearance of hidden time-harmonic structures. Such harmonic structures are represented (at comfortable speed) by the occurrence of the golden ratio as ratio of durations of specific walking and running gait sub-phases. Preliminary experimental evidences suggest that front crawl swimming may behave, under this point of view, like walking and running. This paper aims to demonstrate that a mathematical connection between the golden ratio and the front crawl swimming stroke actually exists, at a pace that plays the role of the comfortable speed in walking and running. Generalized Fibonacci sequences are used to this purpose. They rely on the durations of aggregate phases of the front crawl swimming stroke with a clear physical meaning, while characterizing self-similarity of front crawl strokes in its simple nature and enhanced (stronger) variant. Experimental data on front crawl swimmers illustrate the theoretical derivations, suggesting that the pace playing the role of the comfortable speed in walking and running is the middle/long-distance one, while showing that the self-similarity level increases with the swimming technique and the enhanced self-similarity is associated with the performance of top-level swimmers.

诸如步行和跑步之类的人类运动能够产生有节奏的运动模式，并随之出现隐藏的时谐结构。这样的谐波结构（以舒适的速度）通过黄金比率的出现来表示，黄金比率是特定的步行和跑步步态子阶段的持续时间之比。初步的实验证据表明，在这种情况下，前爬网游泳的行为可能像步行和跑步。本文旨在证明，黄金比率与前爬泳冲程之间确实存在数学联系，其步伐起着舒适的步行和跑步速度的作用。广义斐波那契数列用于此目的。他们依靠前爬泳行程总阶段的持续时间，并具有明确的物理意义，同时以简单的性质和增强的（更强的）变体来表征前部爬行笔触的自相似性。前爬网游泳运动员的实验数据说明了理论推导，表明在步行和跑步中起舒适速度作用的速度是中长距离运动，而随着游泳技术和自学程度的提高，自相似水平也随之提高。增强的自我相似性与顶级游泳运动员的表现有关。