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
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.
References
Erdős–Nagy theorem Wikipedia(Text) CC BY-SA