Erdős–Nagy theorem

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The Erdős–Nagy theorem is a result in discrete geometry stating that a non-convex simple polygon can be made into a convex polygon by a finite sequence of flips. The flips are defined by taking a convex hull of a polygon and reflecting a pocket with respect to the boundary edge. The theorem is named after mathematicians Paul Erdős and Béla Szőkefalvi-Nagy.

History[edit]

Paul Erdős conjectured the result in 1935 as a problem in the American Mathematical Monthly, and Szőkefalvi-Nagy published a proof in 1939. The problem has a curious history and had been repeatedly rediscovered, until Branko Grünbaum surveyed the results in 1995. As it turns out, the original proof had a delicate mistake, which has been since corrected.

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