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.

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.

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.

As customers will tell you, overcrowding is a problem on trains. Fortunately, mathematical modelling techniques can help to analyse the changing demands on services through the day. Tim Gent explains.