According to the standard-text-books, an asymptote is a line which meets a curve at two points at infinity, but is not wholly at infinity. Regarded as a flash of mathematical wit the definition is clever and illuminating, but it is far too subtle for a raw student. He may have learnt that to call parallel lines “lines that meet in a point at infinity” is merely a Pickwickian way of saying that they do not meet at all, but, being in a plane, had (so to speak) their chance of meeting and just failed to take it; but even if he understands that, he may still be mystified here. For the asymptote and the curve meet, he is told, at two points at infinity, and who could guess what complicated tragedy of failure that euphemism conceals?