The inclusion of statistics in the school curriculum is generally advocated for two reasons. All citizens need to develop “the habit of disciplined thinking about ordinary affairs in terms of quantities” and many scientists need to learn techniques essential to their special studies. Perhaps a third reason should be added; statistics can be regarded as part of the training of mathematicians.

The present paper is a sequel to two others which have appeared in the Gazette (July, 1941 and December, 1957) and in which the possibility of attacking a number of familiar triangle theorems by cartesian methods was successfully investigated. The same method is here applied to Morley’s and Pascal’s Theorems.

There are two types of problem on impulsive motion which receive a somewhat cursory treatment in most of the standard text books on dynamics. The first, and more elementary, is as follows: Two rods AB and BC are jointed at B and an impulse J is applied to one of them at a certain point. Find the motion. As one of the steps in the solution of this problem we are usually recommended to take moments about the point B. But, we may remark, B is neither a fixed point nor the centre of gravity of the system. How then are we justified in taking moments about this point? This question will be considered in paragraph 2 below.

Recent articles on equations characterising the trigonometric functions ([1], [2]) prompt a consideration of still another equation, which might be classified under the heading of “Students’ Mathematical Mythology” In [3], Mr. Heafford multiplies the “obvious” sin (x + y) = sin x + sin y by the equally “clear” sin (x − y) = sin x − sin y to obtain the (correct!) result, sin (x+y) sin(x − y) = sin2x − sin2y.