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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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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