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.

You might know the famous formula for an area of a circle, but why does this formula work? **Tom Körner**'s explanation really is a piece of cake, served up with a hefty estimate of pi.

One of the many strange ideas from quantum mechanics is that space isn't continuous but consists of tiny chunks. Ordinary geometry is useless when it comes to dealing with such a space, but algebra makes it possible to come up with a model of spacetime that might do the trick. And it can all be tested by a satellite. **Shahn Majid** met up with *Plus* to explain.

Leonhard Euler, the most prolific mathematician of all time, would have celebrated his 300th birthday this year. In this article, the second in a four-part series on Euler and his work, **Abigail Kirk** explores one of the formulae that carry his name.

*Plus* celebrates its tenth birthday this year. Former editor and present executive editor of *Plus*, **Robert Hunt**, explores how maths popularisation in general, and *Plus* in particular, have changed over the last ten years.

Adrian Bird, a performance engineer at Rolls Royce, tells *Plus* that it doesn't matter what anyone else thinks. You can follow your dreams to do maths and it can lead you to the skies.

One thing that will never change is the fact that the world is constantly changing, and differential equations are the way we mathematically describe the changing world around us. In our first Teacher package we bring together all the material on *Plus* that deals with differential equations, including applications in biology, physics, finance, and even football!