## Articles

**Ian Garbett**discusses light attenuation - the way in which light decreases in intensity as it passes through a medium.

**Mark Wainwright**meets the pair and finds out how they did it.

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!

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.

**Steven J. Brams**uses the Cuban missile crisis to illustrate the Theory of Moves, which is not just an abstract mathematical model but one that mirrors the real-life choices, and underlying thinking, of flesh-and-blood decision makers.

**John Dickson**explains what derivatives are, and how they can be both risky, and used to reduce risk.

**Alison Boyle**investigates aperiodic tilings, which have had unexpected applications in describing new crystal structures.

**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.