We start with a geometric definition:

Fig. 1 illustrates the definition and shows a curve, its point of inflection and the inflectional tangent (i.e. the tangent at the point of inflection) which crosses the curve. We can see that the point of inflection occurs where the curve stops bending to the left and starts bending to the right. This leads to a more descriptive definition of a point of inflection as a point where the direction of bending of a smooth curve changes sense.

It sometimes happens that two apparently disparate branches of mathematics come together unexpectedly, so providing convincing evidence of the unity of our subject. A good example is afforded by the family of curves known as B-splines, which play a part in statistics as well as in numerical geometry.

The movement for reform of mathematical education in France, of which the first signs appeared about 1955, had two main objectives:

• (a) to reduce the mis-match which had grown up between contemporary mathematics and mathematical education at all levels;

• (b) to equip all pupils, as far as possible, with a view of mathematics which would enable them to understand and to master the increasing involvement of mathematics across an ever-widening spectrum.

On a recent visit to Cairo I was struck by two matters which may be of interest to other members and their pupils.