What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

Weekly Problem 38 - 2011

Given three concentric circles, shade in the annulus formed by the smaller two. What percentage of the larger circle is now shaded?

Weekly Problem 37 - 2011

Rotating a pencil twice about two different points gives surprising results...

Weekly Problem 36 - 2011

Imagine cutting out a circle which is just contained inside a semicircle. What fraction of the semi-circle will remain?

It is interesting to compare the variety of approaches that students have used to solve it.

This article teaches you how to draw cardiods, limacons, nephroids and ellipses - a lot easier than they sound! All you need is a pair of compasses and a pencil.

Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.