Winternitz's theorem

In geometry, Winternitz's theorem states that a line through the centroid of a convex set in the plane divides the set into two pieces, each of which contains at least 4/9 the area of the total. The bound of 4/9 is achieved by lines parallel to one side of a triangle.[1]

A generalization to higher dimensions is Grünbaum's theorem.[1]

See also

  • Artur Winternitz

References

  1. 1 2 Shyntar, A. and Yaskin, V., 2021. A generalization of Winternitz’s theorem and its discrete version. Proceedings of the American Mathematical Society, 149(7), pp.3089-3104.


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