Curves of Width One and the
Abstract. We consider the problem of finding the
shortest curve in the plane that has unit width. This problem was first posed
as the “river shore” puzzle by Ogilvy (1972) and is related to the
area of on-line searching. Adhikari and Pitman (1989) proved that the optimal
solution has length 2.2782. We present a simpler proof, which exploits the fact
that the width of a polygon does not decrease under a certain convexification
operation.