After looking at how mathematics finds its way into the world of team sports such as football and netball.

After looking at how mathematics finds its way into the world of team sports such as football and netball it’s important to note it is certainly not limited to this. Individual sports too are heavily influenced by the power of probability, mechanics and general arithmetic and none more so than Tennis! Here are 4 ways that mathematics is weaved into Wimbledon (and every other tennis tournament).

1 - TOURNAMENT STRUCTURING

With over 100 players or teams in each of the men’s, women’s and then double’s tournament and each match lasting on average 2-3 hours, clearly the scheduling for a grand slam tournament requires some serious thought. As is often the case, the logic behind this serious thought is in fact just maths. To reduce the number of matches played, most tournaments follow a knockout structure. This restricts the number of competitors to the values in the sequence of the powers of 2, the power to which 2 is raised being how many rounds will then be played. For example both the men’s and ladies singles competitions at Wimbledon consist of 128 players, and so the tournament will have 7 rounds and 127 matches (each match has exactly 1 loser, every player but 1 will lose exactly 1 match).

2 - THE PERFECT SERVE

Every tennis player or fan will be well aware of the importance of their first serve. Top players will serve at over 100 m/ph and the very best will be able to do so 75% of the time. In order to perfect this art mathematics, and more specifically mechanics, is extremely useful. By determining the distance from an extended arm with a racket to the opposite serving line, and the angle require to get over the net, it is possible to calculate the exact optimal angle of projection whilst also taking force into account.

3 - HAWK EYE

Hawk Eye is one of the most sophisticated advancements in modern sport, combining techniques from statistics, geometry and physics to process an image and then predict it’s position in a chosen frame. In Tennis clearly this is the frame when the ball is going to hit the court. This is done using several cameras placed at different angles that record the balls position in high speed, a computer that is programmed to recognise the ball then calculates it’s position within each frame. This is done continually so that Hawk-Eye can build a picture of the balls 3D projection and hence it’s position in the crucial frame.

4 - THE SCORING SYSTEM

The scoring system in Tennis is somewhat unorthodox compared with other sports. Each match is broken into sets, the sets into games and the games scored through the bizarre points structure of 15,30,40. Though seemingly illogical this unique system has quite an impact on the result of the game. It’s possible to win a match despite loosing more points than you win but it’s thanks to this that makes the game more exciting. Comebacks are more likely and it also gives some points far more importance than others keeping the players under pressure and spectators on the edge of their seats!

- Lucy Chats Maths