In his recent article [1] F. J. Budden produced a binary operation on the set R0 of non-zero real numbers that was associative but not commutative, namely

It forms an interesting and topical example in particle dynamics to investigate the effect of a small frictional perturbation on an elliptic orbit. In this paper the frictional force is assumed to be proportional to the square of the velocity and the eccentricity of the orbit is assumed to be small. Formulae are deduced for the rates of change of the major axis and eccentricity of the ellipse in terms of the rate of change of periodic time, numerical values being compared with the rather sparse information on Sputnik I.

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

I suppose that most teachers of Elementary Mathematics, when first they broach the subject of finding the circnrnference of a circle, write on their blackboards for comparison

and draw the conclusion that “as these results agree a far as the third figure, the approxinlatioll π=3 1/7 can reasonably be expected to get the first 3 figures of your answer right.” The purpose of this paper is to allalyse to some extent a few practical rules of this type.

Aim. I take it that the object of teaching mathematics in a boys’ school is to develop, in combination, the power (i) to apply mathematics successfully to matters of human interest, (ii) to appreciate in some measure that ‘realm of order’ (the expression is borrowed from Professor Nunn) in which mathematical ideas exist.

One of the charms of elementary geometry is that there is no theorem so well known but that one may hope to discover improvements or at least interesting variations in the proof; and the same thing is true of the constructions.

In order to decide between variations in these it is necessary to have some way of measuring the complexity of a construction. This is done by counting the number of settings of the ruler or compass and the number of lines or arcs drawn.