pursuit curve

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.
Darryl Nester worked on the problem for three beetles in a triangle, the resulting curves can be seen at the Bluffton College site as animated gif:

notes

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.