Crazy cuts: Dissecting planar shapes into two identical parts

Abstract

We analyze a well known type of puzzle in planar geometry: given a planar shape, it is required to find a cut that divides the shape into two identical parts (up to rotation and translation). Clearly not all shapes can be so dissected and for some shapes that appear in puzzles the cutting curve is quite surprising and difficult to find. In this paper we first analyze the inverse problem of assembling planar shapes from two identical parts having partially 'matching' boundaries and then use the insights gained on this topic to derive an efficient algorithm to solve the dissection puzzle in quite general situations. © 2009 Springer Berlin Heidelberg.