Paper by Erik D. Demaine

Erik D. Demaine, Blaise Gassend, Joseph O'Rourke, and Godfried T. Toussaint, “All Polygons Flip Finitely… Right?”, in Surveys on Discrete and Computational Geometry: Twenty Years Later, edited by J. Goodman, J. Pach, and R. Pollack, Contemporary Mathematics, volume 453, 2008, pages 231–255, American Mathematical Society. Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference, June 18–22, 2006, Snowbird, Utah.

Every simple planar polygon can undergo only a finite number of pocket flips before becoming convex. Since Erdős posed this finiteness as an open problem in 1935, several independent purported proofs have been published. However, we uncover a plethora of errors, gaps, and omissions in these arguments, leaving only two proofs without flaws and no proof that is fully detailed. Fortunately, the result remains true, and we provide a new, simple (and correct) proof. In addition, our proof handles nonsimple polygons with no vertices of turn angle 180°, establishing a new result and opening several new directions.

Copyright held by the authors.

The paper is 19 pages.

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Related papers:
Flips_CCCG2006 (Polygons Flip Finitely: Flaws and a Fix)

See also other papers by Erik Demaine.
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Last updated May 17, 2017 by Erik Demaine.