The general utility of the ‘pigeon hole principle’ (that if n + 1 pigeons are placed in n boxes one of the boxes contains more than one pigeon!) is neatly illustrated by the problem of showing that:

A persistent problem of the mathematics teacher is the motivation of students especially those not particularly interested in numerical work. In this paper we present a notational device for analysing relationships based on binary notation and show its application to the problem of incest. The authors developed this theory in the course of their study of the rabbinic law on this subject and present this application here, though it could be applied to any legal system. It is hoped that the use of this approach may be useful to introduce mathematical modes of thought to previously uninterested pupils.

In this article several combinatorial problems are posed for the partitioning of certain plane figures. The solutions are obtained by means of Euler’s formula for plane graphs or networks, V - E + R = 1, where V is the number of vertices, E is the number of edges, and R is the number of bounded regions of the figure. Being unified by the common thread of Euler’s formula, the sequence of problems forms an interesting unit on solving related problems.

At the time of writing, second class stamps cost 12p and first class 17p. To minimise the amount of change in my pocket I have a preference for buying these stamps in ratios that cost a whole number of pounds.

The impossibility of a prime number formula seems to have entered the mathematical mythology. As I am continually challenged nonetheless to produce such formulae I thought I would invent some elementary ones. To put them in context I’ll first discuss some classic, and some quite recent, results.

How refreshing to read C. D. Collinson’s [1] article in the March 1986 Gazette on the importance of stressing approximations in teaching mechanics. Once students get over their initial scepticism that mechanics has anything to do with the real world, I too find an enthusiastic response from classes invited to contribute their ideas on the sort of approximations and assumptions which have to be made to model a physical situation. Approximations and assumptions are fundamental to the art of mathematical modelling in mechanics and cause more difficulties to students than is often realised; class discussions reveal that many of the problems which students have with mechanics are related to approximations, and such discussions can also bring out some unsuspected fundamental misconceptions. One such misconception, related to approximations, is discussed here and the proposed method of clarification includes developing a little more Collinson’s use of “the linear approximation”.

Graphical Interference can be attractive and it can be disturbing. We might want to live with it or we might want to avoid it, and in this article we see that elementary geometry suffices to analyse the phenomenon so that we can control it as we wish.