Abstract
Abstract
The Wallace-Bolyai-Gerwien theorem states any polygon can be decomposed into a finite number of polygonal pieces that can be translated and rotated to form any polygon of equal area. The theorem was proved in the early 19th century. The minimum number of pieces necessary to form these common dissections remains an open question. In 1905, Henry Dudney demonstrated a four-piece common dissection between a square and equilateral triangle. We investigate the possible existence of a three-piece common dissection. Specifically, we prove that there does not exist a three-piece common dissection using only convex polygons.
Subject
General Chemical Engineering
Reference4 articles.
1. [Abb11] Timothy G. Abbot, Zachary Abel, Dvid Charlton, Erik D. Demaine, Martin L. Demaine, and Scott D. Kominers, Hinged dissections exist, Discrete and Computational Geometry, 2011.10.1007/s00454-010-9305-9
2. [Bol78] Vladimir G. Boltianskii, Hilbert’s third problem, V. H. Winston & Sons, Washington, D.C.; Halsted Press [John Wiley & Sons], New York-Toronto-London, 1978.
3. [Dud08] Henry Dudeney, The Canterbury Puzzles, chapter Solutions, E.P. Dutton, 1908. (pp. 14–143)
4. [Sal07] Paul J. Sally Jr, Judith D. Sally, Roots to Research, American Mathematical Society, 2007.10.1090/mbk/048