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arXiv · 2109.10216

The Fermat-Torricelli Problem in the Projective Plane

Manolis C. Tsakiris·Sihang Xu
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Abstract

We pose and study the Fermat-Torricelli problem for a triangle in the projective plane under the sine distance. Our main finding is that if every side of the triangle has length greater than $\sin 60^\circ$, then the Fermat-Torricelli point is the vertex opposite the longest side. Our proof relies on a complete characterization of the equilateral case together with a deformation argument.

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Manolis C. Tsakiris, Sihang Xu. 2021-09-03. The Fermat-Torricelli Problem in the Projective Plane. https://arxiv.org/abs/2109.10216

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