Paper by Erik D. Demaine

Reference:

Erik D. Demaine, Blaise Gassend, Joseph O'Rourke, and Godfried T. Toussaint, “All Polygons Flip Finitely… Right?”, in Surveys on Discrete and Computational Geometry: Twenty Years Later, edited by J. Goodman, J. Pach, and R. Pollack, Contemporary Mathematics, volume 453, 2008, pages 231–255, American Mathematical Society. Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference, June 18–22, 2006, Snowbird, Utah.

BibTeX

@InCollection{Flips_DCG20,
  AUTHOR        = {Erik D. Demaine and Blaise Gassend and Joseph O'Rourke and
                   Godfried T. Toussaint},
  TITLE         = {All Polygons Flip Finitely\dots\ Right?},
  BOOKTITLE     = {Surveys on Discrete and Computational Geometry:
                   Twenty Years Later},
  SERIES        = {Contemporary Mathematics},
  VOLUME        = 453,
  PUBLISHER     = {American Mathematical Society},
  EDITOR        = {J. Goodman and J. Pach and R. Pollack},
  YEAR          = 2008,
  PAGES         = {231--255},
  NOTE          = {Proceedings of the AMS-IMS-SIAM Joint Summer Research
                   Conference, June 18--22, 2006, Snowbird, Utah.},

  copyright     = {Copyright held by the authors.},
  length        = {19 pages},
  withstudent   = 1,
  replaces      = {Flips_CCCG2006},
  papers        = {Flips_CCCG2006},
}

Abstract:

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 result remains true, and we provide a new, simple (and correct) proof. In addition, our proof handles nonsimple polygons with no vertices of turn angle 180°, establishing a new result and opening several new directions.

Copyright:

Copyright held by the authors.

Length:

The paper is 19 pages.

Availability:

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Related papers:

Flips_CCCG2006 (Polygons Flip Finitely: Flaws and a Fix)