The theorems that follow are mostly well known; the object of this note is to show that they all follow simply from a single argument, whereas they are usually reached from different starting-points.

Algebraic magic squares of order 4, constructed with the numbers 1, 2,… 16, are of three main types.

From the 4 × 4 frame, nine 2 × 2 quadrants may be cut, and the sum of the numbers in these quadrants furnishes the criteria for distinguishing between the various types of magic squares.

This article contains a discussion of the problem considered by Routh and other writers under the general heading “Rocking Stones”, but is restricted to cases which can be treated as problems in two dimensions. Thus Routh writes: “A perfectly rough heavy body rests in equilibrium on a fixed surface; it is required to determine whether the equilibrium is stable or unstable. We shall suppose the body to be displaced in a plane of symmetry so that the problem may be considered to be one in two dimensions.”

The urgent necessity for examining thoroughly the content of the Mathematical Curriculum in all types of schools at the present time is my reason for introducing a subject which is becoming a well-worn one, and I hope that in the course of the afternoon I may be successful in showing you what I believe to be a fresh and more fundamental approach to the problems involved, and that by being provocative I may invite a discussion on a very important question.