Toussaint Proof

All Polygons Flip Finitely . . . Right ?

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 re...

Polygons Flip Finitely: Flaws and a Fix

Every simple planar polygon can undergo only a finite number of pocket flips before becoming convex. Since Erdős 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.

The Erd} Os-nagy Theorem and Its Ramiications

os-Nagy Theorem and its Rami cations Godfried Toussaint School of Computer Science McGill University Montr eal, Qu ebec, Canada June 29, 1999 Abstract Given a simple polygon in the plane, a ip is dened as follows: consider the convex hull of the polygon. If there are no pockets do not perform a ip. If there are pockets then re ect one pocket across its line of support of the polygon to obtain a...

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Open Guard Edges and Edge Guards in Simple Polygons

An open edge of a simple polygon is the set of points in the relative interior of an edge. We revisit several art gallery problems, previously considered for closed edge guards, using open edge guards. A guard edge of a polygon is an edge that sees every point inside the polygon. We show that every simple non-starshaped polygon admits at most one open guard edge, and give a simple new proof tha...