This paper was originally planned as an exposition of finite geometry in a form in which it could be used to illustrate all the work covered in the normal school geometry course. The beginning of it, however, was anticipated by an article for the Gazette by Mr. H. Martyn Cundy (1), which he has kindly allowed me to read before publication. This present paper shows how a coordinate system can be constructed for the geometry described in his article by using the field of residue classes (mod. 5); that is, the Galois field GF(5). A definition of distance is introduced which extends that adopted by Cundy to a form suited to the discussion of a wider range of theorems.

Beginning a new study involves considerations both of strategy and of tactics. The strategic objective is to impart to the study a sense of purpose, to arouse interest in it, to encourage the pupil to accept the challenge which is implicit in the new situation which confronts him. The tactical question involves the choice of method.

So far as strategy is concerned, the older student beginning algebra has no difficulty in recognising its practical importance in science and technology, where the power of its language to exhibit and clarify relational patterns is manifested. The appeal by way of vocational and cultural interests has been made successfully in various popular books for adults and “second-tryers”; these interests simplify the teaching problem, and the teacher can proceed at an early stage to give training in analysis and expression.

There is no doubt that Professor D. E. Littlewood’s stimulating and instructive article on the foundations of Euclidean Geometry will be widely read by teachers of geometry both in the Schools and in the Universities. It is almost equally certain that many of these readers, unfamiliar in the main with the language of transformation groups, will be in danger of being misled by an ambiguous usage of the term motion.

If it proves to be the case that no reader has in fact been misled then this note will harm no one but the critic himself, and I venture to hope that Professor Littlewood will accept this as evidence of my good intentions.