Given a ship with a known constant direction and speed 
, what course should be taken by a chase ship in pursuit (traveling
at speed 
)
in order to intercept the other ship in as short a time as possible? The problem
can be solved by finding all points which can be simultaneously reached by both ships,
which is an Apollonius circle with 
. If the circle cuts the path
of the pursued ship, the intersection is the point towards which the pursuit ship
should steer. If the circle does not cut the path, then
it cannot be caught.
Apollonius Pursuit Problem
See also
Apollonius Circle, Apollonius' Problem, Pursuit Curve, Trawler ProblemExplore with Wolfram|Alpha
References
Ogilvy, C. S. Solved by M. S. Klamkin. "A Slow Ship Intercepting a Fast Ship." Problem E991. Amer. Math. Monthly 59, 408, 1952.Ogilvy, C. S. Excursions in Geometry. New York: Dover, p. 17, 1990.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 126-135, 1999.Warmus, M. "Un théorème sur la poursuite." Ann. de la Soc. Polonaise de Math. 19, 233-234, 1946.Referenced on Wolfram|Alpha
Apollonius Pursuit ProblemCite this as:
Weisstein, Eric W. "Apollonius Pursuit Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ApolloniusPursuitProblem.html