Question

Let Pi
, 1 ≤ i ≤ n, be n distinct points in the plane, no three of which
are in a straight line. Let n ≥ 3. Prove that the shortest closed curve
which goes through all of these points is a simple polygon, meaning a
finite union of edges connected end to end, with each edge sharing each
of its endpoints with exactly one other edge, and no other intersections
of edges....