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• W2020111166 abstract "Given a polygonal region containing a target point (which we assume is the origin), it is not hard to see that there are two points on the perimeter that are antipodal, i.e., whose midpoint is the origin. We prove three generalizations of this fact. (1) For any polygon (or any bounded closed region with connected boundary) containing the origin, it is possible to place a given set of weights on the boundary so that their barycenter (center of mass) coincides with the origin, provided that the largest weight does not exceed the sum of the other weights. (2) On the boundary of any 3-dimensional bounded polyhedron containing the origin, there exist three points that form an equilateral triangle centered at the origin. (3) On the 1-skeleton of any 3-dimensional bounded convex polyhedron containing the origin, there exist three points whose center of mass coincides with the origin." @default.
• W2020111166 created "2016-06-24" @default.
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• W2020111166 date "2014-06-08" @default.
• W2020111166 modified "2023-10-06" @default.
• W2020111166 title "Weight Balancing on Boundaries and Skeletons" @default.
• W2020111166 cites W1516308076 @default.
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• W2020111166 doi "https://doi.org/10.1145/2582112.2582142" @default.
• W2020111166 hasPublicationYear "2014" @default.
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