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Pursuit Curve

\begin{figure}\begin{center}\BoxedEPSF{PursuitCurve.epsf scaled 700}\end{center}\end{figure}

If $A$ moves along a known curve, then $P$ describes a pursuit curve if $P$ is always directed toward $A$ and $A$ and $P$ move with uniform velocities. These were considered in general by the French scientist Pierre Bouguer in 1732. The case restricting $A$ to a straight line was studied by Arthur Bernhart (MacTutor Archive). It has Cartesian Coordinates equation

y = cx-\ln x.

See also Apollonius Pursuit Problem, Mice Problem


Bernhart, A. ``Curves of Pursuit.'' Scripta Math. 20, 125-141, 1954.

Bernhart, A. ``Curves of Pursuit-II.'' Scripta Math. 23, 49-65, 1957.

Bernhart, A. ``Polygons of Pursuit.'' Scripta Math. 24, 23-50, 1959.

Bernhart, A. ``Curves of General Pursuit.'' Scripta Math. 24, 189-206, 1959.

MacTutor History of Mathematics Archive. ``Pursuit Curve.''

Yates, R. C. ``Pursuit Curve.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 170-171, 1952.

© 1996-9 Eric W. Weisstein