spherical geometry

How will the Universe end? In a big crunch? Or a big freeze? It all depends on its shape...

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.

The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics.