A story from geometry shows how developments in mathematics have fundamentally changed the way we think about the world around us.
If a shape has equal sides with 90 degree angles between them then it's a square, right? Well, not quite...
How will the Universe end? In a big crunch? Or a big freeze? It all depends on its shape...
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.
