Emma + racket = a winning formula
BEYOND its rather unusual scoring system Wimbledon might seem an unlikely setting for maths. But, if you need a calculation done quickly, I bet Andy Murray or Serena Williams could give the likes of Carol Vorderman and Rachel Riley a run for their money. For maths is all around us, and nowhere is that more true than at the All England Club.
Ever wondered how Andy figures out his killer drop shots? Or how Serena gets the angle on her savage serve? Or how Hawkeye reveals whether a shot was in as we all clap and hold our breath?
The answer to all three is the same: maths. The manicured lawns and pearly white outfits might seem some distance from the world of equations and algebra.
But Wimbledon actually uses its own formula to calculate seeding positions.
While other tournaments use the world ranking,wimbledon factors in performance on grass too, using actual algebra.
Even the format – where half the players that start each round are knocked out – is a mathematical concept: exponential decay.
Every time Emma Raducanu steps up to serve there is energy involved: the mathematical equation of throwing mass in the air and exerting a force – Emma’s serving arm and power – against it.and that’s before she’s even hit the ball!
Choosing where to place the ball is all about angles. Remember calculating those acute and obtuse angles at school?
Will Emma go down the centre, skipping past her opponent? Or pull them out wide so she has the whole court to hit into?
These are tiny sections of the court, achieved by difficult angles, not only to get the ball in the right place, but to get it over the net and as close to the line as they can.
It’s no surprise really that Emma said that if she didn’t play tennis, she’d like to work in finance because she likes numbers. Tennis is of course about instincts and practice.
The feel of the ball, agility, knowing where and when to hit a shot.
But the laws of physics still apply. As players move from side to side, run to the net, volley, dash back, they are using major mathematical concepts. What we mathematicians call the coefficient of kinetic friction Andy Murray might recognise as simply running about.
And when the ball hits the ground players must judge its coefficient of restitution. When Emma hits a normal forehand, with no spin, the angle of incidence is approximately equal to the angle of reflection. So the angle at which the ball hits the ground, and the one where it leaves the ground, are pretty much the same.
The ball slows down after it bounces due to the impact of landing.
But when Emma slices her way to success or uses top spin, the angles change.
When a ball is hit with top spin, the angle of reflection is lower than the angle of incidence.
The ball is not affected by friction when impacting the surface of the court and the forward spin pushes the ball forward with greater speed after it bounces. To use this to their advantage, tennis players have to be aware of angles, and what shot is most effective against their opponent.
And what about stats? It’s not just the people watching who delight in the fastest serve, most top spin and longest game.
Players and the teams around them carry out in-depth analyses to try to optimise nutrition, sleep and training. And they constantly analyse and research opponents: whether it’s their first-serve percentage or break-points converted where unforced errors occur.
So it is not just about practice and training but about using mathematics to help determine the right sort of practice and training.
HAWKEYE, of course, let’s us all know whether the players have got it right. It uses 10 cameras to track the ball from different angles. But it’s maths that makes it so accurate.the video is divided into triangles (triangulation) which are then combined to predict the trajectory of the ball to within 5mm.
Maths isn’t just everywhere in tennis – it’s in all sports. Football, snooker, darts, you name it.
From the very basic maths needed to recognise that two goals are more than one to the game theory of penalty kicks. So if you were wondering when you would ever use that maths in real life, the answer is that you are always using maths, just not always consciously.
It’s because maths is all around us I support the Protect Pure Maths campaign, established a year ago to promote all maths, explain the importance of maths and ensure the Government keeps promises on maths funding.
So as the second week of Wimbledon gets under way, by all means admire the athleticism of those vying to make it to the final.
But remember, their brains are running complex calculations at the same time. Get it right and there’ll be another big number waiting at the end – £2million in prize money!
‘Players are using major mathematical concepts’
PARENTS fromwymondham High Academy in Norfolk have been grumbling that long trousers are too warm in the summer term and have demanded the boys be allowed to wear shorts. In response the school has said that in line with its gender neutral policy (“something we are very proud of”) both boy and girl pupils can wear skirts or trousers – but not shorts. Makes no sense to me but then I don’t have a gender neutral policy.
How times change.when I was one of the school-run mummies, we used to stand around in the playground in January lamenting the fact that our poor little boys were forced to wear grey flannel shorts in Arctic conditions.they must be soooo cold, we said.why on earth couldn’t they wear long trousers? Some of the more militant mummies took the issue to the headmaster but nothing changed.they certainly weren’t given the option of wearing a pinafore dress and woolly tights like the little girls. But boys never feel the cold so they didn’t actually care at all.
Going into long trousers was once a mark of maturity. Shorts were for weekends and sailing holidays. As the good Lord intended.
Now half the men in Britain dress like toddlers as soon as the sun comes out.
Bring back the crumpled linen suit, I say. Nothing becomes a man more in the summer months.
IT WAS A weekend when the ancient gods of rock walked among us. The Stones in Hyde Park. Sir Paul Mccartney with his chums Dave Grohl and Bruce Springsteen at Glasto. Grohl at 53 was the baby. Most of the others won’t see 70 again. Or 80 in some cases. Of course it was wonderful and these musicians are living legends. Mccartney ascribes his stamina to eye yoga, which sounds easier than press-ups so I may give it a go. But it was left to the great Joe Walsh (above) of The Eagles (the other ageing supergroup that appeared last weekend in Hyde Park) to put it all in perspective. As in: “I had a lot more fun in my 20s in the 70s than I do being in my 70s in the 20s.” Thanks Joe for saying it as it is.