Given a point P that moves (with constant velocity) along a curve C; then the (generalized) pursuit curve is described by a point Q that is always directed towards P.
It was Pierre Bouguer 1) who was the first to study the curve (in 1732).
When above mentioned curve is a straight line, we call the curve a (straight) pursuit curve.
Martin Gardner stated the classic problem of four beetles, chasing
each other, initially located at the vertices of a square. This gives four
logarithmic spirals to the center.
1) He was the French scientist who tried to measure the earth's density using the deflection of a plumb line by (the attraction of) a mountain.