# curvature

If a shape has equal sides with 90 degree angles between them then it's a square, right? Well, not quite...

Since pi is the number of round things, we devote this year's pi day celebrations to...curvature!

Can physics do for maths what maths has done for physics?

Since he Universe is all there is, there's nothing for it to expand into. So what does "expansion" mean?

Following on from our previous article about curvature of lines and surfaces, we now move up to curvature of their higher dimensional equivalent – manifolds.

Curves bring great beauty to our world. But how curvy is a curve?

That geometry should be relevant to physics is no surprise — after all, space is the arena in which physics happens. What is surprising, though, is the extent to which the geometry of space actually determines physics and just how exotic the geometric structure of our Universe appears to be. Plus met up with mathematician Shing-Tung Yau to find out more.

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.

Is the Universe finite, with an edge, or infinite, with no edges? Or is it even stranger: finite but with no edges? It sounds far-fetched but the mathematical theory of topology makes it possible, and nobody yet knows the truth. Janna Levin tells us more.
• Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.