Journal of Geometry

, 100:29 | Cite as

A generalized Winternitz Theorem

  • Prosenjit Bose
  • Paz Carmi
  • Ferran Hurtado
  • Pat Morin
Article

Abstract

We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point \({q \in P}\) such that every half-polygon that contains q contains nearly 1/2(k + 1) times the area of P. We also give a family of examples showing that this result is the best possible.

Mathematics Subject Classification (2010)

51E99 

Keywords

Winternitz’ Theorem Centerpoint Theorem Polygons 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Paz Carmi
    • 2
  • Ferran Hurtado
    • 3
  • Pat Morin
    • 1
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Department of Computer ScienceBen-Gurion University of the NegevBeer-ShevaIsrael
  3. 3.Departament de Matemàtica Aplicada IIUniversitat Politécnica de Catalunya (UPC)BarcelonaSpain

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