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If you've ever redecorated a bathroom, you'll know that there are only so many ways in which you can tile a flat plane. But once you move into the curved world of hyperbolic geometry, possibilities become endless and the most amazing fractal structures ensue. Caroline Series and David Wright give a short introduction to the maths behind their beautiful images.

You might know the famous formula for an area of a circle, but why does this formula work? Tom Körner's explanation really is a piece of cake, served up with a hefty estimate of pi.