Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the first of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses light attenuation - the way in which light decreases in intensity as it passes through a medium.

The idea is this. To start with, you will choose an envelope at random, say by tossing a coin, and look at its contents, which is a cheque for some number - say n. (By randomising like this, you can be sure I haven't subconsciously induced you to prefer one envelope or the other.) You want to make sure that the bigger the number is, the more likely you are to keep it, in other words, the less likely you are to swap.

There are many sorts of games played in a "bunco booth", where a trickster or sleight-of-hand expert tries to relieve you of your money by getting you to place bets - on which cup the ball is under, for instance, or where the queen of spades is. Lots of these games can be analysed using probability theory, and it soon becomes obvious that the games are tipped heavily in favour of the trickster!

Bill Casselman writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.
This pattern with kite-shaped tiles can be extended to cover any area, but however big we make it, the pattern never repeats itself. Alison Boyle investigates aperiodic tilings, which have had unexpected applications in describing new crystal structures.
Sometimes a mathematical object can be so big that, however disorderly we make the object, areas of order are bound to emerge. Imre Leader looks at the colourful world of Ramsey Theory.