## For Students

### Mathematics Circle

A mathematics circle describes a group of young mathematicians who meet regularly to engage collaboratively in mathematical thinking.

Our mathematics circle meets once each fortnight, on Mondays from 5-7pm. The focus of the meetings will be to develop skill in problem solving and in mathematical investigation. You'll also have fun making friends and having a regular setting for doing maths with your peers.

Here are some examples of the sorts of problems we’ll look at:

1. Is the number 22225555 + 55552222 divisible by 7?
2. A cake is cut with a knife poisoned on one side. Prove that however many cuts we make, there will always be a piece of cake free of poison.
3. What combinations of regular polygons will tessellate the plane?

Some of the problems we'll look at will enable us to study ideas that are not only interesting in their own right, but that are also helpful for solving Olympiad-style questions.

Applying to the Mathematics Circle

We only have room for a small number of participants in our maths circle, and we need to know that you’ll be interested in, and will benefit from, the sort of maths we intend to do.

To apply to join the mathematics circle, you must be in year 11 or below, and you will need to attempt and solve as many of the admissions problems that as you can. These questions aren't easy - they are designed to get you to think and to try a few different things. Most of them will require you to persevere - they are hard enough that a solution might not come to you at once.

What we are most interested in is not “the answer” but how you get to the answer. You will need to write up your solutions and in that write up you will need to show us your line of thought. For example, if you think the answer to 4b) is yes, then you need to justify your answer - how would you convince one of your friends that this is the correct answer, and that there isn't a collection of 10 numbers (not all the same) that satisfy the conditions?

Here are some other pointers:

1. By all means discuss these problems with friends, but write up your own answers, in your own words (and diagrams, if these help). Maths is not a spectator sport!
2. We certainly don't expect you to try and solve all of them; pick a few that you like the look of and put some concentrated thought into those. You will be much more likely to make a breakthrough, than if you jump around trying all the questions at random.
3. If you get stuck on a question, you may want to play around with it and see whether you can make some useful observations. For example, in question 6 you can explore what happens with different kinds of triangles, and see if you can generalise to any triangle.
4. Conversely, if you breeze through a question, you should check that your method is watertight and works in all cases (this is especially relevant in this is especially relevant in question 8, where your proof has to consider all possible cuttings, and not just the ones in the diagrams).
5. Lastly, have fun! One of the reasons why we enjoy maths is because it is fun and we can explore a lot of different things. It's not always about what the correct answer is, and you may enjoy the problems more if you run them through your head over a span of days.

Applications for this academic year have now closed.

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