In team sports such as football, rugby, handball and basketball, players' positions are governed by geometric considerations. Christian Gourcuff, currently the coach of Algeria and well known as the former coach of Lorient, is also a mathematics teacher. His approach to football reflects this, as this interview he gave to Libération in 1998 shows:
"I try to establish a geometric organization of play. It is based on controlling space. At first, I was criticized on the grounds that this system stifled creativity. I remain convinced that organization actually enhances creativity. Eight players form a unit. It moves as a screen for the player in possession. Ideally, equal distances would be maintained between all the players in the unit. This distance can be estimated at around 15 metres. It is a fairly rigorous system, and it carries risks. If the gaps between the players suddenly grow too wide, the network unravels and the organization collapses. Conversely, if the organization remains intact, the runs are shorter and consequently less energy is expended. Certain aspects of this organization can also be found in basketball."
Christian Gourcuff goes on to explain that his players are arranged in two straight lines moving diagonally towards the opposing goal. The hardest part is maintaining this formation when falling back. Of course, the system should not be too rigid, so that players can take advantage of opportunities, but this kind of geometric formation recurs in every team ball sport.
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The referee's geometry
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