Analytical Solution for the Generalized Fermat-Torricelli Problem

Alexei Yu. Uteshev

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arXiv · 1208.3324

Analytical Solution for the Generalized Fermat-Torricelli Problem

Alexei Yu. Uteshev

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Abstract

We present explicit analytical solution for the problem of minimization of the function $ F(x,y)= \sum_{j=1}^3 m_j \sqrt{(x-x_j)^2+(y-y_j)^2} $, i.e. we find the coordinates of stationary point and the corresponding critical value of $ F(x,y) $ as functions of $ {m_j,x_j,y_j}_{j=1}^3 $. In addition, we also discuss inverse problem of finding such values of $ m_1,m_2,m_3 $ with the aim for the corresponding function $ F $ to posses a prescribed position of stationary point.

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Alexei Yu. Uteshev. 2012-08-16. Analytical Solution for the Generalized Fermat-Torricelli Problem. https://arxiv.org/abs/1208.3324

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