Polygons Flip Finitely: Flaws and a Fix

Every simple planar polygon can undergo only a finite number of pocket flips before becoming convex. Since Erdos posed this as an open problem in 1935, several independent purported proofs have been published. However, we uncover a plethora of errors and gaps in these arguments, and remedy these problems with a new (correct) proof. 1 Pocket Flips Given a simple polygon in the plane, a pocket is a maximal connected region interior to the convex hull and exterior to the polygon. A (pocket) flip is the reflection of a pocket, or more precisely the subchain of the polygon bounding the pocket, across its line of support, the bounding edge of the convex hull. In 1935, Paul Erdos [3] introduced the problem of simultaneously flipping all pockets of a simple polygon, and repeating this process until the polygon becomes convex. He conjectured that this process terminates after a finite number of steps. In 1939, B

• Type: Conference
• Year: 2006
• Where: CCCG
• Authors: Erik D. Demaine, Blaise Gassend, Joseph O'Rourke, Godfried T. Toussaint
• Keywords: CCCG 2006, CCCG 2007, Finite Number, Pocket, Polygon