Marcus du Sautoy talks about football, cryptography, and numbers.
In the first part of this article we let maths set the scene for a free kick. Now we continue the drama, tracing the trajectory of the ball throughout the milliseconds it takes it to reach the goal line.
Free kicks will deliver much of the drama in the football world cup this summer. But how should strikers approach them and how does the design on the ball impact on its behaviour in flight? Maths can give us answers...