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 theory of duality is well known as a useful tool in the study of convex three-dimensional polyhedra. For example, if we know the types of polyhedra that can be circumscribed about a sphere, duality provides an immediate answer to the question as to what types can be inscribed in a sphere. Theorems like Euler’s Theorem (V – E + F = 2 where V, E and F are the numbers of vertices, edges and faces of a convex polyhedron) are self-dual in the sense that duality simply interchanges the values of V and F.

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”.

I was interested to see in a recent issue of the Gazette a note from Hoare and Wright [1] about the distribution of leading significant digits, l.s.d., and “Benford’s Law” that this distribution is logarithmic. This distribution has fascinated many people since Benford’s original observation [2] in 1938 of the dirty pages at the beginning of a book of log tables.

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.