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Heilbronn’s Problem of Eight Points in the Square

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Abstract

In this work the authors consider the problem of optimally distributing 8 points inside a unit square so that the smallest area of the \(\left(\begin{array}{c}8\\ 3\end{array}\right)\) 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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Correspondence to Zhenbing Zeng.

Additional information

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.

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Dehbi, L., Zeng, Z. Heilbronn’s Problem of Eight Points in the Square. J Syst Sci Complex 35, 2452–2480 (2022). https://doi.org/10.1007/s11424-022-1220-7

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  • DOI: https://doi.org/10.1007/s11424-022-1220-7

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