{"paper":{"title":"Analytical Solution for the Generalized Fermat-Torricelli Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alexei Yu. Uteshev","submitted_at":"2012-08-16T09:37:39Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3324","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}