16

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.

1. The Ramsey number R(2,5)

This is the number that will answer the question, "how many people do we need, to be sure of having either two friends, or five strangers?"

But of course, if there are any two people in the room who know each other, that gives us our two friends. On the other hand, if not, then all the people in the room are mutual strangers. So as long as there are five people, there must be either two friends or five strangers.

To show that, even with only nine points, there must be either a blue triangle or four points connected by red lines, we need a subtle improvement on the reasoning we used for 10 points.

Perigal bibliography

• On geometric dissections and transformations in volume 1 of The Messenger of Mathematics and On geometric dissections and transformations II. in volume 2 of The Messenger of Mathematics (1874-5), both by Henry Perigal.

This issue's topics

• New maths column
• Gyros lighter while spinning
• Longest number
• Softball teams problem

New maths column

From Dean Browell <browells@earthlink.net>

Just an F.Y.I. that a new section and article with a mathmatic skew has debuted in the online magazine Skewed Perspective.

Topic of the month

• Fear of maths - a self-fulfilling prophecy

Have you anything to say on this or other subjects of interest to Plus readers? E-mail plus@maths.cam.ac.uk.