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On the Heilbronn Optimal Configuration of Seven Points in the Square

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Automated Deduction in Geometry (ADG 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6301))

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Abstract

In this paper, we prove that for any seven points in a unit square there exist three points whose area is not greater than a constant h 7 = 0.083859... as conjectured by Francesc Comellas and J. Luis A. Yebra in 2002.

This work is supported by the National Natural Science Foundation of China (No. 10471044) and the Major Research Plan of the National Natural Science Foundation of China (No. 90718041).

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Author information

Authors and Affiliations

  1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, 200062, Shanghai, China

    Zhenbing Zeng & Liangyu Chen

Authors
  1. Zhenbing Zeng
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  2. Liangyu Chen
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Editor information

Editors and Affiliations

  1. Max-Planck-Institut für Informatik, RG 1: Automation of Logic, 66123, Saarbrücken, Germany

    Thomas Sturm

  2. Wilhelm-Schickard-Institut für Informatik, Symbolic Computation Group, Universität Tübingen, 72076, Tübingen, Germany

    Christoph Zengler

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Zeng, Z., Chen, L. (2011). On the Heilbronn Optimal Configuration of Seven Points in the Square. In: Sturm, T., Zengler, C. (eds) Automated Deduction in Geometry. ADG 2008. Lecture Notes in Computer Science(), vol 6301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21046-4_11

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  • DOI: https://doi.org/10.1007/978-3-642-21046-4_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21045-7

  • Online ISBN: 978-3-642-21046-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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