MATHEMATICS OF JIPTO: and research topics
by Grigori Tomski


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JIPTO (Jeux Intellectuels de Poursuite de Tomski /Tomski&#x2019;s Intellectual Pursuit Games) is a large family of board games developed from the game &#x22;Sonor&#x22; which has four very similar main versions: JIPTO-B1-A1, JIPTO-B1-A1, JIPTO -B1-A1, JIPTO-B1-A1. The &#x22;Sonor&#x22; models the pursuit of the five &#x22;fugitives&#x22; by a &#x22;pursuer&#x22;. The &#x22;fugitives&#x22;, concentrated at the beginning of the game on one side of the board, try to reach the other side of the board avoiding being touched by the &#x22;pursuer&#x22;; He tries to capture the &#x22;fugitives&#x22; as far away as possible from his ship. The JIPTO plateau is divided into three main zones by lines I, II, III. Each &#x22;fugitive&#x22; who, before being captured, reaches one of these lines, marks one point per line reached.<br />The process of building the different versions of JIPTO is based on the progressive complication of the rules: each game thus created generates several games corresponding to the modifications and complications of the rules. Some modifications create a more or less perceptible complication of an earlier version, while the others are real transformations which allow, for example, on the basis of the intellectual versions of the JIPTO to create versions of the JIPTO of reasoned chance or the cooperative versions (so you can play JIPTO with several partners).<br />I developed with my disciples the JIPTO theory which provides an inexhaustible number of unresolved mathematical problems of pursuit, formulated in the language of elementary mathematics. This subject is described in the books currently available in digital format on Amazon's sites:<br />Grigori Tomski, G&#xe9;om&#xe9;trie &#xe9;l&#xe9;mentaire de la poursuite, Editions du JIPTO, 2005. <br />Grigori Tomski, Talents math&#xe9;matiques: Syst&#xe8;me de d&#xe9;tection pr&#xe9;coce et infaillible, 2016.<br />These books will soon be translated into English.<br />The discovery of the existence of an area of mathematical research within the reach of high school and college pupils at the time of the great professionalization of mathematical research is unexpected and must be of interest to all specialists in education and of the popularization of mathematics.<br />Thus, if one succeeds in attracting the attention of the gifted pupils to the irresolute mathematical problems of the elementary geometry of pursuit, they can be initiated into true scientific research. This is certainly the most effective method of detecting future professional mathematicians.<br />The teaching of mathematics is mainly aimed at developing reasoning and logical reflection, to cultivate the possibilities of abstraction. It brings rigor into thought and stimulates the imagination. Mathematics facilitates international communication and is a strong component of culture. Therefore, this book is accessible and useful for many readers, for example:<br />- The clairvoyant parents who are concerned about creating a solid foundation for the education and success of their children.<br />- Creative mathematics teachers who want to test the abilities of their students on real mathematical problems, which require real hard research, rather than the tasks of the Olympiads and other mathematical contests.<br />- Students who wish to test their ability in professional mathematical activities, to start quickly a real mathematical research in order to train their mind and character to succeed in the major fields of of modern science, and to obtain in mathematics a real chance to write earlier than others and to support quickly a thesis.<br />- For students looking for mathematical thesis themes or on the teaching of mathematics and their popularization. In our book are thousands of subjects formulated for this research.<br />