Is there maths in soccer

Answer 1

The task of a goalkeeper also involves geometry:

Think of the following problem: if an attacking player is approaching the goalkeeper, where does the goalkeeper need to stand to have the best chance of preventing a score?

A good goalkeeper does not stand on the goal line too much of the time. He stays a bit in front of his goal, because it makes no sense to dive behind the goal line to "save" a ball. When a single attacker is approaching him, he will try to be on the angle bisector of the lines from that player to the goal posts. He will turn his body toward the approaching player, so that when he dives to the side to stop a shot, he is as far from the left-hand side as from the right-hand side.

There also are interesting dilemmas for the goalkeeper about how far he should stand in front of his goal: when he is far from his goal the goalkeeper can get a single player's ball more easily, but the attacking player can also more easily lob the ball over the goalkeeper. And when a second player is coming at the same time, that player has a free path to the goal. See related link for more information.