# A generalized Winternitz Theorem Academic Article

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### 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.

### publication date

• September 17, 2011