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

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 Plus anniversary year — A word from the editors

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

The work of Donald Coxeter, who died on 31 March 2003, will continue to inspire both mathematicians and artists.

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.