Issue 16

 September 2001 What colour is my hat? Why do we always seem to recognise faces? And what happens when you join up the midpoints of all of the sides of a triangle? Explore all this and more in this issue of Plus.
 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. 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. This is a game played between a team of 3 people (Ann, Bob and Chris, say), and a TV game show host. The team enters the room, and the host places a hat on each of their heads. Each hat is either red or blue at random (the host tosses a coin for each team-member to decide which colour of hat to give them). The players can see each others' hats, but no-one can see their own hat. Plus talks to Christine Hogan, programmer, sysadmin and author, now studying aerodynamics and hoping to become a member of a Formula One team. Similar triangles and colouring the plane The very fetching purple and yellow packaging states that this is "the" interactive geometry software. A little optimistic, perhaps; The Geometer's Sketchpad and Cabri both have their - not insubstantial - followings. And the previous release of Cinderella gave the impression of a terribly well-featured package lacking slickness. But therein lies the value of Version 1.2: slickness. Avid readers of popular books on the laws of nature are tolerably familiar with a number of facts. They know that electricity, magnetism and the weak force between elementary particles have been unified, that Einstein's theory of special relativity arose from an attempt to reconcile Newtonian mechanics with the laws of electromagmetism, and that his later theory of general relativity had something to do with the structure of spacetime. Money is peculiar stuff. It has no use of any kind apart from its value in exchange for something else, and this grows over time as it earns interest, or shrinks as inflation overtakes it. If you have money to invest, there are a bewildering array of different kinds of financial instrument available: interest-bearing accounts, bonds, pension funds, stocks and shares, options ... Robin J Wilson's book is "not", as he assures the reader in the Preface, "a history of mathematics book in the conventional sense of the word". No indeed. It is, rather, a selective account of aspects of the history of mathematics which have appeared on postage stamps from across the world.