Mathématisation élémentaire de l'action dans les jeux sportifs

[摘要] The aim of this article is to show that the analysis of players’ motor action can be formalized mathematically, particularly with the help of graphs and matrixes. A traditional game, la Galine, is chosen as the common theme to illustrate in practical terms the concepts and options successively put forward. The motor logic or internal logic of the game, gives objective indicators relative to space, objects, time and others, which allow us to identify sociomotor roles precisely. Sociomotors roles can be organized in a transition graph which illustrates the players’ potential choices. The same reasoning is used to draw graphs of sociomotor sub-roles’ changes. One can deduct game graphs and players’ decision trees. This approach is generalized and a classification of games based upon the morphology of their sociomotor roles network, is put forward. The main idea is to convert the pertinent ludomotor characteristics in a graph structure, and to exploit this graph’s elementary but exact mathematical properties, for psychological and sociological interpretations.

[学科分类] 数学（综合）

[关键词] sporting game;modelling;motor action;transition graph;sociomotor role;internal logic;games graph