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MC 2019: Maple in Mathematics Education and Research pp 307–323Cite as

A Heilbronn Type Inequality for Plane Nonagons

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1125))

Abstract

In this paper, we present a proof of the property that for any convex nonagon \(P_1P_2\ldots P_9\) in the plane, the smallest area of a triangle \(P_{i}P_{j}P_{k} (1\le i< j < k \le 9)\) is at most a fraction of \(4\cdot \sin ^2(\pi /9)/9= 0.05199\ldots \) of the area of the nonagon. The problems is transformed into an optimization problem with bilinear constraints and solved by symbolic computation with Maple.

Supported by the National Natural Science Foundation of China (No. 11471209).

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Zhenbing Zeng, Jian Lu & Lydia Dehbi

  2. East China Normal University, Shanghai, 200062, China

    Liangyu Chen

  3. Henan University, Henan, 475001, China

    Jianlin Wang

Authors
  1. Zhenbing Zeng
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  2. Jian Lu
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  3. Lydia Dehbi
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  4. Liangyu Chen
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  5. Jianlin Wang
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Corresponding authors

Correspondence to Jian Lu , Lydia Dehbi or Jianlin Wang .

Editor information

Editors and Affiliations

  1. Maplesoft, Waterloo, ON, Canada

    Jürgen Gerhard

  2. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias Kotsireas

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Zeng, Z., Lu, J., Dehbi, L., Chen, L., Wang, J. (2020). A Heilbronn Type Inequality for Plane Nonagons. In: Gerhard, J., Kotsireas, I. (eds) Maple in Mathematics Education and Research. MC 2019. Communications in Computer and Information Science, vol 1125. Springer, Cham. https://doi.org/10.1007/978-3-030-41258-6_23

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  • DOI: https://doi.org/10.1007/978-3-030-41258-6_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-41257-9

  • Online ISBN: 978-3-030-41258-6

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