It is proposed to discuss in this paper some properties of the general Frégier-point and point out its connections with well known conics like the Apollonian hyperbola and the nine-point conic of a quadrangle. Incidentally, we discover a pedal conic of a quadrangle which has very intimate relations with the nine-point conic.

The motivation for this article was the desire to make the cosine rule in some way geometrically “obvious”. What we have ended up with is a mixture of inductive and deductive approaches which we hope goes some way to illuminating the cosine rule, and to enhancing students' relational understanding of it. The germ of these ideas can be sown soon after students have met Pythagoras, with the question “O.K., suppose the triangle ABC is not rightangled: what can we say about a2, b2 and c2 now?”

1. The present paper is an attempt to sketch a mode of procedure for teaching Limits and Convergence to beginners. It is felt by many teachers that at present

(1) the subject is introduced too academically;

(2) that its Arithmetical foundation is not brought into sufficient prominence;

(3) that therefore pupils leave school with only a very hazy notion of what it is all about;

Provided one of the integers m and n is even, it is obvious that an m × n rectangle can be covered with 1/2mn dominoes, each domino covering two unit squares. If some of the dominoes are oriented in each of the two possible ways, it is possible that there may be no continuous straight line of domino edges, either horizontal or vertical, across the rectangle: in other words, each of the (m — 1) + (n — 1) fault lines on the underlying grid is crossed by at least one domino. Such rectangles are called fault-free, and are mentioned by S. Golomb in [1] where the concept is attributed to R. I. Jewett. An example with m = 6, n = 8 is shown in Fig. 1.