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arXiv · 1406.7779

Analytical solution of the weighted Fermat-Torricelli problem for tetrahedra: The case of two pairs of equal weights

Anastasios N. Zachos
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Abstract

The weighted Fermat-Torricelli problem for four non-collinear and non-coplanar points in the three dimensional Euclidean Space states that: Given four non-collinear and non-coplanar points A1, A2, A3, A4 and a positive real number (weight) Bi which correspond to each point Ai, for i = 1,2,3,4, find a fifth point such that the sum of the weighted distances to these four points is minimized. We present an analytical solution for the weighted Fermat-Torricelli problem for tetrahedra in the three dimensional Euclidean Space for the case of two pairs of equal weights.

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Anastasios N. Zachos. 2014-06-27. Analytical solution of the weighted Fermat-Torricelli problem for tetrahedra: The case of two pairs of equal weights. https://arxiv.org/abs/1406.7779

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