The number of the Mathematical Association’s new headquarters in London Road, Leicester is 259.

This number has some quite interesting features. It is for instance the sum of the three squares

32 + 52 + 32 × 52,

and the sum of four cubes

23 + 23 + 33 + 23 × 33 and 13 + 23 + 53 + 53.

All teachers of mathematics are aware of variations both in notation and definitions between different books; in addition, the conventions used in science often differ from those used in mathematics. Readers may have seen the Royal Society booklet Quantities, units and symbols and the report SI units, signs, symbols and abbreviations issued by the Association for Science Education. A sub-committee of the Mathematical Association’s Teaching Committee has been studying this subject with the aid of examples and proposals submitted by members.

When I started teaching real analysis to first-year college of education students, I thought that at least I ought to be consistent in what I said. When I told the students what a word meant, I thought they ought to hear the same story as they heard from my colleagues who were teaching other branches of mathematics. I even thought I ought to tell them something like what they would find in a consensus of the real analysis books they might look at. I knew that I ought not to use different meanings for the same word on different occasions. Alas . . .

Some time ago I had the opportunity to pay a visit to Farawaystan to study how they treated different educational questions. In the following I am going to tell about my strange experiences. One of the first lessons I attended was in tool science. Here is a section from the textbook:

“3.1 definition. A screwdriver is a metal cylinder, of which one end is flattened and the other end is fixed in a cylinderlike, stiff material, whose surface is not smooth. If the material cylinder is rotated through an angle a, the metal cylinder will rotate through an angle b in the same direction and of the same size as a. The diameter of the metal cylinder is smaller than that of the material cylinder. The material cylinder is often called the handle.

Call the ends of a ruler A and Z, and (towards A) place on it a mark X. Draw a line BC the length of AX, and a square BCDE. Erect a perpendicular bisector of BC. With centre C and radius CE draw a circle. Now place the ruler (Fig. 1) so that AZ passes through B, with A on the perpendicular bisector of BC, and with X on the circle. Then ∠BAC = π/7.

The aim of coding theory is not to deceive, but to make information impervious to errors in transmission. When messages are being transmitted along wires, the likelihood of mistakes in transmission is small. When messages are being transmitted by radio, lightning can distort reception. When messages such as television pictures are being transmitted across interstellar space, there is a substantial possibility, because of meteorites, that the message received will differ from the message transmitted.

During and after World War II, operational research teams needed new, computer-adaptable methods for optimization problems in industry, engineering, economics and the armed forces. The calculus methods developed in the sixteenth century to solve problems in astronomy, physics and geometry, even when they were applicable, were not always computer-adaptable. Among these new operational research methods is geometric programming, an optimization technique which in its beginning utilized the theorems in this article. The word “geometric” comes from its use of the geometric mean as well as geometrical concepts such as orthogonality and normalization.

The slogan which forms the title of this note was coined in the 1960s by the opponents of large scale university expansion. It was maintained that an increase in student numbers could only lower academic standards. The purpose of this note is to show that more can mean better or worse according to the criterion used. The theorems proved in the main part of the paper give formal statements of intuitively obvious results, but the amount of misunderstanding generated on this topic suggests that such an exposition is worthwhile. The conclusion of the note must be that comparisons of academic achievement, based on varying proportions admitted to higher education, should be interpreted with great care.

In the June 1974 edition of the Mathematical Gazette Dr. C. W. Puritz gave an interesting description of a school-room exercise on the calculation of π and some associated numerical error analysis. This note suggests some further relevant material which his pupils might also find interesting and instructive.

There are occasions when one needs to know the North and one’s latitude, as for example when one is constructing and orientating a sundial, or exploring in unknown terrain.

A method of obtaining this information by observing the sun is here described, which does not possess the disadvantages of that in which one observes the sun when its altitude is greatest—namely of being useless if the sun is obscured by cloud at noon or if the sun’s declination is not known. It is suitable for a classroom experiment, and is an application of stereographic projection.