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Opinion
Topics of the month
- Hanging on a chad - voting systems and presidential elections
- One-two-three cheers - wear your maths on your sleeve
Have you anything to say on these or other subjects of interest to Plus readers? E-mail plus@maths.cam.ac.uk.
Plus Magazine

Yes, you were right to wish you were in the other lane during this morning's commute! Nick Bostrom tells why we're usually caught in the slow lane.
Plus Magazine

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.
The mathematics of Fibonacci's sequence
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
Answers
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.
Nine points will do
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.
Bibliography
Perigal bibliography
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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.
Notes and queries
Notes and queries
Opinion
Topic of the month
There is no editorial this month
Opinion
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.