
Given a dog (P) chasing a
pedestrian (Q). The
anxious human creature runs in a straight line, with constant speed u. The dog runs also
with a constant speed (v), always in the direction of its prey. The path the dog runs has
been given the name pursuit curve. The ratio u/v of the two velocities is
just the value of the parameter 'a' in the formula ^{1)}. Leonardo da Vinci was the first to consider this problem. Arthur Bernhart studied the curve. Realize that this pursuit curve (for a=1) is not the tractrix: equal distance between pursued and pursuer is not equivalent with equal speed between them. 1) the tangent to the curve of pursuit can be expressed
as dy/dx = (y  ut) / (x 1) (i) 2) To understand that holds: ^{ } 