On the Traversing of Geometrical Figures

Abstract

SUPPOSE that an outline figure of any kind is drawn upon a blackboard. In its construction the chalk describes a certain number of closed or open paths, a path being defined as the mark made by the chalk during the whole time of any one of its contacts with the board. But the number of paths thus actually described is not necessarily the smallest by which the figure can be produced, and it is an interesting problem to analyse a given figure into its minimum number of paths, each traversed once. As a simple example, let two oval paths be drawn intersecting in four points; the resulting figure can be traversed as one closed path. If two of the intersections are joined, the new figure can be traversed as one open path; if the remaining intersections are joined, the figure cannot be reduced to less than two paths.

On the Traversing of Geometrical Figures.

By J. Cook Wilson. Pp. x + 154. (Oxford: Clarendon Press, 1905.) Price 6s. net.