A generalized Winternitz Theorem Academic Article uri icon


  • 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.

publication date

  • September 17, 2011