hyperbolic geometry
How will the Universe end? In a big crunch? Or a big freeze? It all depends on its shape...
The 19th century experienced a geometrical revolution. Find out how the new geometries that were discovered shaped philosophy, science, culture and art.
Did you learn at school that the angles in a triangle always add up to 180 degrees? If yes then your teacher was wrong. Find out why here.
Squares do it, triangles do it, even hexagons do it — but pentagons don't. They just won't fit together to tile a flat surface. So are there any tilings based on fiveness? Craig Kaplan takes us through the five-fold tiling problem and uncovers some interesting designs in the process.
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.
Mathematicians and artists mingle in London
The work of Donald Coxeter, who died on 31 March 2003, will continue to inspire both mathematicians and artists.