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 o...

Full description

Saved in:
Bibliographic Details
Main Authors Tsakiris, Manolis C, Xu, Sihang
Format Journal Article
LanguageEnglish
Published 03.09.2021
Subjects
Mathematics - Metric Geometry
Online AccessGet full text

Cover

More Information
Summary: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.
DOI:10.48550/arxiv.2109.10216