TY - JOUR
AU - Tsakiris, Manolis C.
AU - Xu, Sihang
PY - 2022/12/04
Y2 - 2023/01/30
TI - The Fermat-Torricelli problem in the projective plane
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 128
IS - 3
SE - Articles
DO - 10.7146/math.scand.a-133419
UR - https://www.mscand.dk/article/view/133419
SP -
AB - <p>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.</p>
ER -