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The Curve of Pursuit

Published online by Cambridge University Press:  03 November 2016

C.C. Puckette
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Abstract

Find the path taken by a ship which pursues, and always directs its course towards, another ship (supposed moving in a straight line), their speeds being constant and in fixed ratio, and their initial directions at right angles.

Type
Research Article
Information
The Mathematical Gazette , Volume 37 , Issue 322 , December 1953 , pp. 256 - 260
Copyright
Copyright © The Mathematical Association 1953

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References

* Historical details taken mainly from Enc. Britt. (1947) and the histories of F Cajori and D. E. Smith. Bouguer introduced the signs ≥ and ≤ (Cajori). He is best known for his measurement of a degree of the meridian near the equator, a work which occupied him some ten years.

page no 256 note * A copy of this volume may be seen in the Birmingham Central Library (their ref. 18820).

* In Professor H. W Turnbull’s book, Mathematical Discoveries of Newton, there is (p. 26) a quotation from De Analysi which mentions “mechanical” curves. The New English Dictionary has the following note : “Applied to curves not expressible by equations of finite and rational algebraic form=transcendental. So called as admitting of production only by ‘mechanical construction’” The final phrase is explained as “construction by the use of some apparatus as distinguished from ‘tracing’ by calculation of successive points.”

page no 257 note * Reprinted in Math. Gazette, XV, No. 214, Note 1004.

page no 257 note * Also derived in Math. Gazette, XV, No. 208, p. 160 : method essentially the same as Bouguer’s.

page no 257 note * Of the many sources consulted, only two refer to Maupertuis in this connection, namely, Peacock, Calculus, and Amer. Math. Monthly, (loc. cit.). Even Cajori and Smith fail to mention him.

* Without acknowledgment, save in the cases cited. Bouguer is usually mentioned as the source of the problem.

page no 258 note * Except for C. Cailler, Intro. Géom. à la Mécanique Rationnelle (p. 508), who derives no particular solution, but provides a neat method of obtaining the general differential equation. (I am indebted to Professor Broadbent for this reference and for a copy of Cailler’s method.)

page no 258 note * More correctly, Frenet formulae, first given by F Frenet (1847).

* Tait and Steele, loc. cit.

page no 260 note * Noticed by Bouguer.

page no 260 note * See, for example, Edwards, , Diff. Calc., p. 357 Google Scholar