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Heilbronn's Problem of Eight Points in the Square

DEHBI Lydia1,2, ZENG Zhenbing2   

  1. 1. School of Software Engineering, East China Normal University, Shanghai 200062, China;
    2. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • Received:2021-06-25 Revised:2021-10-26 Online:2022-11-25 Published:2022-12-23
  • Contact: ZENG Zhenbing,Email:zbzeng@shu.edu.cn
  • Supported by:
    This research was supported by the National Natural Science Foundation of China under Grant Nos. 12171159 and 12071282, and "Digital Silk Road" Shanghai International Joint Lab of Trustworthy Intelligent Software under Grant No. 22510750100.

DEHBI Lydia, ZENG Zhenbing. Heilbronn's Problem of Eight Points in the Square[J]. Journal of Systems Science and Complexity, 2022, 35(6): 2452-2480.

In this work the authors consider the problem of optimally distributing 8 points inside a unit square so that the smallest area of the ${8\choose 3}$ triangles formed by them is maximal. Symbolic computations are employed to reduce the problem into a nonlinear programming problem and find its optimal solution. All computations are done using Maple.
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