The Magic Points in the Triangle

Xingyu Pan No.2 High School of East China Normal University

S.-T. Yau High School Science Awarded Papers mathscidoc:1608.35146

Dongrun-Yau Science Award, 2013
I heard the concept of the ”equal‐sum point” in a math summer camps and found it very interesting. After searching on the Internet,I found that the ”equal‐sum point” was associated with Soddy point. Soddy point is a magic point in plane geometry, which was found by British physicist, chemist Frederick.Soddy. Some research about the Soddy point has been done in foreign countries, but the properties are not comprehensive. In China, Teacher HuasongHuang raised the concept of the “equal‐sum point” and the “equal‐difference point” and drew some properties, I found that these two points were very similar to the Soddy point, but they did not link the two points with Soddy point. In this article ,I will connect the Soddy point with the “equal‐sum point” and the “equal‐difference point” and study their properties more deeply and find some new discoveries.
Soddy point , Soddy circle ,equal‐sum point, equal‐difference point, properties
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@inproceedings{xingyu2013the,
  title={The Magic Points in the Triangle},
  author={Xingyu Pan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160818150133067381240},
  booktitle={Dongrun-Yau Science Award},
  year={2013},
}
Xingyu Pan. The Magic Points in the Triangle. 2013. In Dongrun-Yau Science Award. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160818150133067381240.
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