投影平面上的Fermat-Torricelli问题

Pub Date : 2021-09-03 DOI:10.7146/math.scand.a-133419

M. Tsakiris, Sihang Xu

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引用次数: 0

摘要

我们提出并研究了正弦距离下投影平面上三角形的费马-托里拆利问题。我们的主要发现是，如果三角形的每条边的长度都大于sin60 ^ circ，那么费马-托里切利点就是最长边对面的顶点。我们的证明依赖于对等边情况的完整描述以及变形论证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Fermat-Torricelli problem in the projective plane

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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