Euclidean geometry

3-sphere

We can't visualise it, but we can still think about it! And there are clever ways of glimpsing what it might look like.

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

In normal life higher dimensions smack of science fiction, but in mathematics they are nothing out of the ordinary.

How will the Universe end? In a big crunch? Or a big freeze? It all depends on its shape...
So easy to describe, yet so hard to prove.
The 19th century experienced a geometrical revolution. Find out how the new geometries that were discovered shaped philosophy, science, culture and art.
This article explores how Euclid's ancient geometry interacts with all aspects of human thought and life.
The impossible becomes possible when you move into the third dimension.
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.
Keats complained that a mathematical explanation of rainbows robs them of their magic, conquering "all mysteries by rule and line". But rainbow geometry is just as elegant as the rainbows themselves.

The Plus anniversary year — A word from the editors