The diagonal system of control(DSC) is the main system used by the referees for positioning on the football field.
Mathematically, this system provides the best way available to cover the pitch so that the right decisions can be easily taken by the referees.
DSC is imposed as a standard method by Sir Stanley Rous- former referee and President of FIFA from 1961 to 1974.
According to this system, the two assistant referees move along the half court, located diagonally opposite to each other, while the referee covers all the pitch, moving diagonally from one part to the other uncovered by the assistants part of the field.
This allows the referee to officiate in a fluid motion without needing to turn his back to the play, stop, and then turn around sharply.
Looking at the diagram above, it is clear that in terms of geometry, this is the best way to cover the ground by the referees.
We are once again convinced that mathematics has a great influence on football. Knowledge in math and its applications make the football game so spectacular and attractive.
People like Ottmar Hitzfeld, Dennis Bergkamp, Johan Cruyff have achieved great success in football not only because of their great talents, but because they have understandings for the rules of mathematics.