Variety in Tangents and Normals

Extract

We seniors are apt to be told that, in our teaching of analytical geometry, we have been in the habit of giving too much attention to the intricacies of conic sections, and that work on other curves and their tangents and normals would have been more interesting and instructive. There is much force in this criticism, but when we come to examine the alternatives to the conics which are offered to us, they are usually cubic curves, probably given in terms of parameters, such as the “Folium of Descartes” I should like to suggest that some better-known curves, notably the curve of sines and the logarithmic curve, will provide examples even more instructive than the “Folium”, and that these examples have at least the advantage of greater novelty.