The Research on Circle Family and Sphere Family

Chen Yan The Affiliated High School of South China Normal University Ziquan Zhuang The Affiliated High School of South China Normal University

S.-T. Yau High School Science Awarded Papers mathscidoc:1608.35024

2009
A circle family is a group of separate or tangent circles in the plane. In this paper, we study how many parts at most a plane can be divided by several circle families if the circles in a same family must be separate (resp. if the circles can be tangent). We also study the necessary conditions for the intersection of two circle families. Then we primarily discuss the similar problems in higher dimensional space and in the end,raise some conjectures.
Circle Family; Structure Graph; Sphere Family; Generalized Inversion
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@inproceedings{chen2009the,
  title={The Research on Circle Family and Sphere Family},
  author={Chen Yan, and Ziquan Zhuang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160813215155097350072},
  year={2009},
}
Chen Yan, and Ziquan Zhuang. The Research on Circle Family and Sphere Family. 2009. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160813215155097350072.
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