# hyperbolic geometry

If a shape has equal sides with 90 degree angles between them then it's a square, right? Well, not quite...

As we are well over half way through advent, we thought today we'd look towards the future of the Universe

Akshay Venkatesh has been awarded the Fields medal 2018 for his work exploring the boundaries of number theory.

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.