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How is maths related to sports?
By Eva:

I am very curious to find out about how maths is related to sports. I know about why runners set off at different positions, but i don't know how to explain this and what is the theory behind this and other things.I hope you can reply my question soon. Thank you.

By Richard (rpd25) on October 20, 1998:

Dear Eva,

This is a very general question as maths is related to everything in all kinds of ways. When you talk about relating maths to sport you are talking about something called applied maths. Applied maths is when you use maths to find out things about the real world. The other main type of maths is called pure maths, which has nothing to do with the real world at all.

When you do sums, say 5+6, you are doing pure maths as the numbers 5 and 6 alone are meaningless to the real world. But if you asked, how many oranges do I have if I have 5 oranges in one hand and six in the other, you are asking an applied maths question.

If you do much more maths you will soon learn the difference.

Now back to your question.

A couple of interesting ways maths is related to sport:

When someone throws a javelin, hammer, discus or shot-put, at what angle should they throw it to make it go furthest? You can see that the angle will matter, as if they throw it horizontally, it will not go far, and if they throw it straight up it will not go anywhere. It turns out that the best angle is 45 degrees above the horizontal.

If you have to go somewhere and it is raining, do you get less wet if you walk or if you run? If you walk it takes longer, so you get rained on more, but if you run, you run into drops of rain as they fall and so get wetter. The answer to this is rather complicated and depends upon many things, you might like to think what they are. If you are interested though, it's usually better to run.

These are just a couple of examples, it's hard to give an idea of how widely maths relates to everything, but believe me it does.

The reasons runners start a different positions is because the track they run on is oval, and to start with they must run in lanes.

Start by thinking of the track as circular, and each runner having to run along a circle, in the middle of their lane say. The circles must be inside each other, so they must be different sizes. You can see that the runners on the outside will have further to go, because they are running round bigger circles, so they are given a headstart.

If you know the equation for the distance round a circle when its radius is r, you might like to try to find out how much of a headstart the runners should have on a circular track. You will need to decide first how big the track is, and how wide the lanes are and also how many times the runners must go round.

If you need any help on this, please ask again.

Best wishes,
Richard.