ACADEMIC TALK
Watch the lecture by Dr Tom Crawford below and don’t forget to take a look at the extra resources and have a go at the activity at the end.
How to take the perfect penalty
Dr Tom Crawford
You may be a great football player on the pitch, but did you know that some mathematical equations worked out from the sidelines can help improve your performance in penalties?
We thought this would be a good opportunity to explore sport from an angle you might not have thought much about before: the Mathematics of Sport! In these talk, Dr Tom Crawford looks at how maths can be used to model various features of two of the world’s most popular sports: football and athletics.
In this talk, Dr Crawford looks at the maths of penalties in a game of football, using Pythagoras’ Theorem, quadratic equations and other mathematical techniques to try to work out how to take the perfect penalty kick.
Further Reading
Here’s a short introduction to mathematical modelling. If you would like to challenge yourself and look at a university-level introduction to mathematical modelling, try this.
If you would like to find out more about the University of Bath’s research into penalties, click here or watch this video.
Using the techniques shown in this lecture, try to apply geometry to find a perfect move in a different sport – perhaps the perfect tennis serve, or the perfect rugby penalty.
Show your workings alongside your final answer.
Pick a situation that has as few varying factors as possible, as it will make the modelling easier – for example, it is easier to model a penalty kick than a normal goal because it has fixed rules about movement and distance.
If you need to find measurements similar to a goalie’s diving range, you can either estimate or record your own!
Make sure you research important information such as the shape of the net or the size of the pitch.
Remember, the way to do mathematical modelling is to turn a real world situation into maths, solve the maths, then apply this solution to the real world!
