
Journal for Geometry and Graphics 19 (2015), No. 1, 031042 Copyright Heldermann Verlag 2015 Two New Analytical and Two New Geometrical Solutions for the Weighted FermatTorricelli Problem in the Euclidean Plane Anastasios Zachos Department of Mathematics, University of Patras, Greece azachos@gmail.com We obtain two analytic solutions for the weighted FermatTorricelli problem in the Euclidean Plane which states: given three points in the Euclidean plane and a positive real number (weight) which correspond to each point, find the point such that the sum of the weighted distances to these three points is minimized. Furthermore, we give two new geometrical solutions for the the weighted FermatTorricelli problem (weighted FermatTorricelli point), by using the floating equilibrium condition of the weighted FermatTorricelli problem (first geometric solution) and a generalization of Hofmann's rotation proof under the condition of equality of two given weights (second geometric solution). Keywords: Weighted FermatTorricelli point, floating case, absorbed case, median, ruler and compass construction. MSC: 51M04; 51M16, 51M15, 74P20 [ Fulltextpdf (211 KB)] 