curvature
Following on from our previous article about curvature of lines and surfaces, we now move up to curvature of their higher dimensional equivalent – manifolds. 
From a smile to a line drawing by Picasso, 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 ShingTung 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 farfetched but the mathematical theory of topology makes it possible, and nobody yet knows the truth. Janna Levin tells us more.
