The Gleaning on p. 427 of The Gazette for December, 1965, has produced three notes on a very individual teacher. In an age when “aids” flourish, we do well to return from time to time to the teacher in the class-room, on whom everything depends. These notes are printed in full (apart from introductions) as a tribute to the past and as an encouragement to the eccentrics of the present.

In certain computer applications to engineering problems such as the automatic control of machine tools the computing equipment derives its input in digital form, from, for example, an angle-indicating device on a rotating shaft. The indicating device may take the form of a multiple commutator or a coded disc read by photoelectric means. Since the shaft is rotating at mechanical speeds and the reading device is operating at electronic speeds a possibility of false readings exists when for example a change from 1999 to 2000 is taking place. In fact any of the readings 1999, 1990, 1900, 1000 or 2000 may occur in the same sort of way that a mileage recorder could be misread under similar circumstances.

Although the gradient of a scalar, and the curl and divergence of a vector can be obtained by various elementary methods in terms of curvilinear components and coordinate vectors, the corresponding results for the components of strain and the vector divergence of stress are usually obtained by specializing the formulae for covariant derivatives. The purpose of this note is to give an elementary approach to these latter results in the spirit of the theory of Cartesian tensors. Apart from standard elementary vector analysis the only prerequisite is a geometrical appreciation of the analysis of deformation. For completeness an elementary analytical derivation of the results about gradient, curl and divergence is given first by a method which, whilst certainly not new, does not appear to be very well known.

The recent introduction of logic and group theory in the secondar; schools has inspired many young students to investigate these area of modern science. The purpose of this paper is to bind togethe propositional logic and the theory of symmetric groups in a elementary fashion so that new vistas may be revealed to those wh wish to explore.

In a sense Stirling’s formula can be adapted to slide-rule computation of x! when a; is a fraction and tables are not at hand.

The interest of a survey of motivation in mathematics among girls first became apparent at a Ministry of Education conference in Cambridge in August 1963 when, among other subjects, new syllabuses in mathematics were discussed. These had been designed by men teaching in boys’ schools.

Kendall and Moran, in introducing their book on Geometrical Probability (Griffin, 1963), give as illustrations three solutions of a problem due to Bertrand, that of finding the probability that a “random chord” of a circle is longer than the side of the inscribed equilateral triangle. The first solution regards the random chord as being generated by the two points on the circumference which it joins, and which are uniformly and independently distributed. In the second the chord is assumed to have a fixed direction perpendicular to a given diameter, and its point of intersection with this is uniformly distributed over the diameter. In the third, the foot of the perpendicular from the centre is uniformly distributed over the circle. The probabilities in these three cases are respectively ⅓, ½, and ¼.

(1) Definitions. In the system of n coplanar straight lines each line is produced indefinitely in both directions so that all possible points of intersection (vertices) are obtained. The plane of the system is thus divided into regions which may be closed (of finite extent) or open (of infinite extent).

An interesting application of elementary matrix theory is to prove that at any point of a rigid body there exists at least one set of principal axes of inertia.

If p is a prime and ps is the greatest power of p that divides N!, then

We are concerned with the problem of constructing on a sphere maps whose faces (regions) all have the same number of edges.

In this note we prove the following Theorem pertaining to Format’s Last Theorem.