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.

Additional Metadata
Keywords Centerpoint Theorem, Polygons, Winternitz' Theorem
Persistent URL dx.doi.org/10.1007/s00022-011-0076-0
Journal Journal of Geometry
Citation
Bose, P, Carmi, P. (Paz), Hurtado, F. (Ferran), & Morin, P. (2011). A generalized Winternitz Theorem. Journal of Geometry, 100(1-2), 29–35. doi:10.1007/s00022-011-0076-0