Location of the Fermat-Torricelli medians of three points

Benítez, Carlos; Fernández, Manuel; Soriano, María

doi:10.1090/S0002-9947-02-03113-6

Location of the Fermat-Torricelli medians of three points
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by Carlos Benítez, Manuel Fernández and María L. Soriano PDF

Trans. Amer. Math. Soc. 354 (2002), 5027-5038 Request permission

Abstract:

We prove that a real normed space $X$ with $\dim X\ge 3$ is an inner product space if and only if, for every three points $u,v,w\in X$, the set of points at which the function $x\in X\to \|u-x\|+\|v-x\|+\|w-x\|$ attains its minimum (called the set of Fermat-Torricelli medians of the three points) intersects the convex hull of these three points.

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