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Asymptotes

Published online by Cambridge University Press:  03 November 2016

T. P. Nunn
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Extract

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?

Type
Research Article
Information
The Mathematical Gazette , Volume 13 , Issue 182 , May 1926 , pp. 97 - 103
Copyright
Copyright © Mathematical Association 1926

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References

page 99 note * See p. 52 of the translation by D. E. Smith and M. L. Latham (Open Court Series, 1925).

page 102 note * I owe the rest of (9) to Professor Neville, to whom I am indebted for helpful criticisms of the first draft of this article.