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Plus Magazine

Sep 2001
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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.

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The mathematics of Fibonacci's sequence

Nov 2001

The Fibonacci sequence is defined by the property that each number in the sequence is the sum of the previous two numbers; to get started, the first two numbers must be specified, and these are usually taken to be 1 and 1. In mathematical notation, if the sequence is written (x0,x1,x2,...) then the defining relationship is xn=xn1+xn2(n=2,3,4...) with starting conditions x0=1,x1=1.

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Answers

Sep 2001

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.

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Bibliography

Sep 2001

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.

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