what is a curve of pursuit?

Answer 1

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. Pursuit curves were considered in general by the French scientist Pierre Bouguer in 1732, and subsequently by the English mathematician Boole.

Under the name "path minimization," pursuit curves are alluded to by math genius Charlie Eppes in the Season 2 episode "Dark Matter" of the television crime drama NUMB3RS when considering the actions of the mysterious third shooter.

The equations of pursuit are given by
(A-P)/(|A-P|).(P^.)/(|P^.|)=1,

which specifies that the tangent vector at point P is always parallel to the line connecting A and P, combined with
P^..P^.=1,

which specifies that the point P moves with constant speed (without loss of generality, taken as unity above). Plugging (2) into (1) therefore gives
((A-P).P^.)/(|A-P|)=1.

Answer 2

I'm guesing this question is inspired by Numb3rs?

See the source below.