Weight balancing on boundaries and Skeletons

Luis Barba, Otfried Cheong, Jean Lou De Carufel, Michael Gene Dobbins, Rudolf Fleischer, Akitoshi Kawamura, Matias Korman, Yoshio Okamoto, János Pach, Yuan Tang, Takeshi Tokuyama, Sander Verdonschot, Tianhao Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationProceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014
PublisherAssociation for Computing Machinery
Pages436-443
Number of pages8
ISBN (Print)9781450325943
DOIs
Publication statusPublished - 2014
Event30th Annual Symposium on Computational Geometry, SoCG 2014 - Kyoto, Japan
Duration: Jun 8 2014Jun 11 2014

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Other

Other30th Annual Symposium on Computational Geometry, SoCG 2014
CountryJapan
CityKyoto
Period6/8/146/11/14

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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  • Cite this

    Barba, L., Cheong, O., De Carufel, J. L., Dobbins, M. G., Fleischer, R., Kawamura, A., Korman, M., Okamoto, Y., Pach, J., Tang, Y., Tokuyama, T., Verdonschot, S., & Wang, T. (2014). Weight balancing on boundaries and Skeletons. In Proceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014 (pp. 436-443). (Proceedings of the Annual Symposium on Computational Geometry). Association for Computing Machinery. https://doi.org/10.1145/2582112.2582142