| Polygonal Chains: from Pocket Flipping to Protein Folding (2008) | |||||||||||||||
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| Although polygonal chains—open chains of rigid links connected at joints—are the simplest type of bar-andjoint linkage, they nevertheless have both a wide range of applicability and a rich mathematical structure leading to intriguing computational questions. It is characteristic and apt that, in a sense, this area of investigation was initiated by Paul Erdős in 1935, with a problem he posed in the American Mathematics Monthy [Erd35]. He asked whether every polygon may be convexified by a finite number of simultaneous “pocket flips. ” The answer was provided in a later issue by de Sz. Nagy [dSN39], who proved that, restricting to one flip at a time, a finite number of flips suffice to convexify any polygon. Toussaint has shown how this theorem has been rediscovered over the years since [Tou99], but a close examination has revealed that none of the proofs are entirely sound, including Nagy’s original. I will present a recent proof developed in collaboration | |||||||||||||||
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