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

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

3 被引用数 (Scopus)

抄録

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.

本文言語英語
ホスト出版物のタイトルProceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014
出版社Association for Computing Machinery
ページ436-443
ページ数8
ISBN(印刷版)9781450325943
DOI
出版ステータス出版済み - 2014
外部発表はい
イベント30th Annual Symposium on Computational Geometry, SoCG 2014 - Kyoto, 日本
継続期間: 6 8 20146 11 2014

出版物シリーズ

名前Proceedings of the Annual Symposium on Computational Geometry

その他

その他30th Annual Symposium on Computational Geometry, SoCG 2014
国/地域日本
CityKyoto
Period6/8/146/11/14

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • 幾何学とトポロジー
  • 計算数学

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