# List by Author: Ken Bray

Hitting the spot

What's the best spot to aim a penalty at?

Blink and you'll miss it: The free kick in football (part II)

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.

Blink and you'll miss it: The free kick in football (part I)

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...

When is a goal not a goal?

Remember Frank Lampard's disallowed goal in the 2010 World Cup match against Germany? The ball hit the crossbar, landed well behind the line but then bounced out again. And it all happened too quickly for the ref to spot it was a goal. How these kind of (non)-goals happen and what can we do about them?

A fly walks round a football

What makes a perfect football? Anyone who plays or simply watches the game could quickly list the qualities. The ball must be round, retain its shape, be bouncy but not too lively and, most importantly, be capable of impressive speeds. We find out that this last point is all down to the ball's surface, the most prized research goal in ball design.

If you can't bend it, model it!Learn about the aerodynamics of footballs and perfect your free kick.
• Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.