Tilings have adorned buildings from ancient Rome to the Islamic world, from Victorian England to colonial Mexico. But while it sometimes seems free from worldly limitations, tiling is a very precise art, where not much can be left to chance. We can push and turn and wiggle, but if the maths is not right, it isn't going to tile. Josefina Alvarez and Cesar L. Garcia investigate.
The computer animation used in movies and games is now so lifelike, it is very hard to believe that you are actually watching a surface built from simple shapes of triangles. Phil Dench tells Plus how he uses mathematics to help bring these models to life.
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.
One of the many strange ideas from quantum mechanics is that space isn't continuous but consists of tiny chunks. Ordinary geometry is useless when it comes to dealing with such a space, but algebra makes it possible to come up with a model of spacetime that might do the trick. And it can all be tested by a satellite. Shahn Majid met up with Plus to explain.