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Improved Euler’s inequalities in plane and space

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Abstract

We improve Euler’s inequality \(R \ge 2r\) where R and r are triangle’s circumradius and inradius, respectively. It involves symmetric functions of triangle’s sidelengths. We also prove non-Euclidean versions of this result. Next, we refine 3D analogue of Euler’s inequality \(R \ge 3r\) for tetrahedra and briefly discuss recursive way to improve Euler’s inequality for simplices.

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  1. Department of Mathematics, University of Zagreb, Bijenička 30, 10000, Zagreb, Croatia

    Darko Veljan

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  1. Darko Veljan
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Correspondence to Darko Veljan.

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Veljan, D. Improved Euler’s inequalities in plane and space. J. Geom. 112, 31 (2021). https://doi.org/10.1007/s00022-021-00595-2

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  • DOI: https://doi.org/10.1007/s00022-021-00595-2

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