The eminent physicist, Peter Guthrie Tait, having constructed mathematical models of the flight of a golf-ball and having carried out an extensive series of experiments to evaluate their parameters, specified the maximum distance a golf ball could be made to carry by the most accomplished golfer. He was then upstaged by his son who hit a monumental drive which pitched even further. The golfing press of the day - what there was of it - was happy to run the story and scientists themselves seemed to enjoy the joke at Tait’s expense. Macfarlane, for example, related the anecdote in the following terms in a lecture delivered just eight months after Tait’s death:

When students first meet Simpson’s rule, we look for simple applications to show them what it can do. I don’t imagine I am the only teacher who has suggested using it to find a numerical value for π - which up until then they have always had to take on trust.

There have been three obvious paradigms which have successively dominated mathematics teaching during my teaching career: three eras of predominant pedagogy. None of the so-called “reforms”, however, achieved a total take-over of the schools. “Traditional mathematics”, the first paradigm, survived right through the era of “new maths for schools”, the second paradigm. In some schools “new maths” was hardly noticed, and probably in no school did “new maths” change everything in the curriculum – there were a number of topics which carried on much as before. Applicable/problem-solving maths, the third paradigm, arrived on the back of Shell, Spode, Cockcroft and SMP 11-16 around 1982.

Coincidences are a source of amusement and occasional unease in our lives. They often appear to defy the laws of probability – even to demand a supernatural “explanation”. Probability theory reveals the root cause of this disparity between expectation and reality. As I shall show, it stems from the fact that our intuitive estimate of the probability of a coincidence occuring becomes increasingly inaccurate the more “outlandish” the coincidence seems to be.

Some time ago a friend, who was organising a chess league, rang me up and asked “How many different ways are there of arranging a roundrobin league tournament?” Thinking of his phone bill I told him I’d ring him back. Which was just as well, because the problem was much more difficult dian I had realised. Indeed it is unsolved in general. In the language of graph theory it is the problem of finding the number of onefactorisations of a complete graph. These and related objects have been the focus of considerable study both in combinatorics and recreational mathematics and, although the enumeration question remains unanswered in general, it is, even for small numbers of players, remarkably full of interest.

Schools run by local authorities have an annual budget which is calculated by formula. The formula used for funding my school is quite easy to understand and its components all seem reasonable, yet it can cause some unexpected problems for an unwary manager.

Most of the funding depends on the number of pupils, each being worth an annual amount according to his or her age. If a comprehensive school has fewer than 750 pupils it is regarded as being small, needing extra money to provide an adequate curriculum. This extra is given as a bonus for each pupil; and tapers to zero as the numbers reach 750.

Cheryl Maiden is director of the Maths 100 Foundation, which is based in Henley-on-Thames.

The day begins before 9.00 a.m. and it’s a relaxed time opening mail over breakfast, punctuated by the occasional call. This morning it’s a query from the printers about the paper for Part 3, and the Yellow Pages again. I enjoy the post as it has become increasingly varied, bringing interesting new people into the Maths 100 project.

The cubic holds a double fascination, since not only is it interesting in its own right, but its solution is also the key to solving quartics. This article describes five fundamental parameters of the cubic (δ, λ, h, xN, and yN), and shows how they lead to a significant modification of the standard method of solving a cubic, generally known as Cardan’s solution.