The Fermat-Torricelli problem in the projective plane

IF 0.3 4区数学 Q4 MATHEMATICS

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

M. Tsakiris, Sihang Xu

引用次数: 0

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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投影平面上的Fermat-Torricelli问题

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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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.