## curvature of space

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.

Space is the stage on which physics happens. It's unaffected by what happens in it and it would still be there if everything in it disappeared. This is how we learn to think about space at school. But the idea is as novel as it is out-dated.

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.

**Sir Martin Rees**gives

*Plus*a whistlestop tour of some of the more extraordinary features of our cosmos, and explains how lucky we are that the universe is the way it is.

**Professor Kip Thorne**shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.

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.

*Plus*is a special, marking the occasion of Stephen Hawking's 60th birthday. Plus attended his Birthday Conference in Cambridge, where we interviewed some of the world's most influential mathematicians and physicists.