hyperbolic geometry

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.

Lucinda Mathews visualises tricky surfaces

The Plus anniversary year — A word from the editors

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.
Mathematics illustrates the forefront of visualising science
Mathematicians and artists mingle in London