# Issue 43

 June 2007 If you thought you knew what geometry is all about, then this issue of Plus may change your mind. We explore a strange point-less geometry of spacetime, find out about hyperbolic geometry's amazing fractals, celebrate a geometric formula named after Leonhard Euler, the most prolific mathematician of all time, and try to calculate pi. This issue also contains the first ever Plus teacher package and, to celebrate our tenth birthday, continues our series on the history of Plus.
 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. 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. 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. 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. Geometry is power Plus 100 —the best maths of the last century More maths grads 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! Have a go at this Plus-themed Sudoku variation. Sylvia Nasar told the story of John Nash's troubled life in her book A Beautiful Mind, although probably better known as the film with Russel Crow. I suspect maths in primary school would be greeted with far more enthusiasm if students had Ian Stewart as a teacher. Any man who can explain electromagnetism, gravity and atomic nuclear forces in terms of a piggy fridge magnet and a smashed kitchen plate is, surely, a communicator to be reckoned with. The basis of this wonderful book came in a series of questions about modern maths sent to Philip Davis by a friend of his, Christina.