Two-hand Dissections of Orthogonal Polygons

Irena Pashchenko

 

Two polygons A and B of the same area are two-hand dissectable if A may be partitioned into two sets which can be rigidly rearranged to form B. Dissections have been studied for a hundred years, mainly as recreational mathematics. I implemented an algorithm to find a dissection, if one exists, between two orthogonal polygons, ones whose edges are horizontal or vertical. The algorithm was designed by Professor O'Rourke together with a group of researchers at the University of Waterloo.

An example is shown in the figure below. The task is to two-hand dissect A to form the 10x10 square B (top row). The surprising unique dissection found by my program is shown below (bottom row), with one piece shown shaded and the other white.

We are now working on k-hand dissections.

Advisor: Joseph O'Rourke

Supported by a grant from the National Science Foundation.