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A sharp estimate for the hexagonal circle packing constants

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Abstract

In [6] it is shown that the hexagonal circle packing rigidity constants s n satisfy

$$\lim_{n\rightarrow \infty}ns_n=\displaystyle{\frac{2\sqrt[3]{2} \Gamma^2({1}/{3})}{3\Gamma({2}/{3})}}.$$

In this paper we further prove that

$$s_n=\frac{2\sqrt[3]{2} \Gamma^2({1}/{3})} {3\Gamma({2}/{3})} \frac{1}{n}+O\left(\frac{1}{n^2} \right).$$

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Authors and Affiliations

  1. Institute of Mathematics, AMSS, Chinese Academy of Sciences, 100190, Beijing, People’s Republic of China

    Zhengxu He & Jinsong Liu

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  1. Zhengxu He
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  2. Jinsong Liu
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Correspondence to Jinsong Liu.

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He, Z., Liu, J. A sharp estimate for the hexagonal circle packing constants. Geom Dedicata 146, 193–210 (2010). https://doi.org/10.1007/s10711-009-9433-7

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  • DOI: https://doi.org/10.1007/s10711-009-9433-7

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