# Articles

Rogue trading?The dangers of trading derivatives have been well-known ever since they were catapulted into the public eye by the spectacular losses of Nick Leeson and Barings Bank.

**John Dickson**explains what derivatives are, and how they can be both risky, and used to reduce risk.
From quasicrystals to KleenexThis 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.
On the dissecting table

**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.
Friends and strangersSometimes 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.Faster than light

Scientists at the NEC Research Institute in Princeton have carried out an experiment in which a pulse of light appeared to emerge from a cloud of gas before it even entered.

Death and statisticsActuarial science began as the place where two branches of mathematics meet: compound interest and observed mortality statistics. Financial planning for the future is therefore rooted firmly in the past.

**John Webb**takes us through some of the mathematics involved, introducing us to some of the colourful characters who led the way.
Fishy business'Of the myriad strategems I employ to avoid useful work, the one I most enjoy is to envision how scientists of earlier eras would have made use of modern computers.'

**John L. Casti**tells us how today's mathematicians are using computers to carry on the work of turn-of-the-century polymath d'Arcy Wentworth Thompson, who showed how mathematical functions could be applied to the shape of one organism to continuously transform it into other, physically similar organisms.
Take a breakThere are many errors that can occur when numbers are written, printed or transferred in any manner. Luckily, there are schemes in place to detect, and in some cases even correct, such errors almost immediately.

**Emily Dixon**takes a break and discovers that codes are not just for sleuths.Mathematical mysteries: The Solitaire Advance

Solitaire is a game played with pegs in a rectangular grid. A peg may jump horizontally or vertically, but not diagonally, over a peg in an adjacent square into a vacant square immediately beyond. The peg which was jumped over is then removed.

In perfect harmonyThe harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem.

**John Webb**applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.
Emmy Noether: Against the oddsA brief look at Emmy Noether's challenging journey to become one of the twentieth century's great
mathematicians.