Football fever

England may have bombed out, but the Euro 2016 Championships are still in full swing. Here are some articles by our favourite football expert, Ken Bray, exploring the maths of football from all angles. Maybe the England team, and all other footballers too, should brush up on their maths!

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Hitting the spot at the Euros
A little geometry goes a long way in working out the best spot to aim a penalty at.


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How to take the perfect penalty
"It's failure to prepare mentally and failure to take practicing penalties really seriously." This is Ken Bray's explanation for England's dismal performance in penalty shootouts. Bray, who also wrote the article above, talks some more about penalties in this video.


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Blink and you'll miss it: The free kick in football
Free kicks deliver much of the drama in football. But how should strikers approach them and how does the design on the ball impact on its behaviour in flight? Ken Bray give us some answers...


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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?


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A fly walks around a football
What makes a perfect football? It 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.


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If you can't bend it, model it
Learn about the aerodynamics of footballs and perfect your free kick.