A generalized Winternitz Theorem

Prosenjit Bose, Paz Carmi, Ferran Hurtado, Pat Morin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ε 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.

Original languageEnglish
Pages (from-to)29-35
Number of pages7
JournalJournal of Geometry
Issue number1-2
StatePublished - 1 Apr 2011


  • Centerpoint Theorem
  • Polygons
  • Winternitz' Theorem

ASJC Scopus subject areas

  • Geometry and Topology


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