A Heilbronn Type Inequality for Plane Nonagons

  • Zhenbing Zeng
  • Jian LuEmail author
  • Lydia DehbiEmail author
  • Liangyu Chen
  • Jianlin WangEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1125)


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.


Heilbronn problem Convex nonagon Computer algebra Lagrange multipliers 


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Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiChina
  2. 2.East China Normal UniversityShanghaiChina
  3. 3.Henan UniversityHenanChina

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