Curves of Minimum Width and the Asteroid Mapping Problem

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We consider two geometric puzzles. First a three dimensional generalization to the well known "Sailor-in-the-Fog" puzzle. In this problem, a spaceship starting from the surface of a spherical asteroid must survey the entire surface of the asteroid. The objective is to find the shortest path from which all points in the surface are visible. We present a set of candidate solutions including a best-known-so-far curve of length 6.04 times the intial depth of the diver. In the second part, we solve the river shore open problem by Ogilvy which asks for the shortest path of width one.

Bibtex Entry