This is outside the scope of the problems I was referring to. I just meant problems of dissecting a polygon into n congruent pieces. It's a cute problem, though. Franklin T. Adams-Watters -----Original Message----- From: Schroeppel, Richard <rschroe@sandia.gov> I think the example below requires pieces with a circular boundary, that can't be polygonized. Take a square, and remove a smaller interior square, oriented at an angle of atan(1/2). Also remove a small notch along one side, and toward a corner. The goal is to dissect this into the same larger square, but with the smaller square hole + notch rotated to make the orientation parallel to the larger square. The minimal piece-count solution (2) is to just cut a circular piece that includes the small square, and rotate it. --------------- | | | ---- | | < | | | | | | | ---- | The goal polygon. | | | | --------------- Rich -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com on behalf of ... I think it's true that if a polygon has a dissection in the latter form, it has one into polygons, but I don't know if that has been proved. My intuition is that you can take any curved edges and approximate them by piecewise linear edges, getting a polygon; but I don't see how to make that rigorous. ___________________________________________________ Try the New Netscape Mail Today! Virtually Spam-Free | More Storage | Import Your Contact List http://mail.netscape.com