{"paper":{"title":"Is it possible to determine a point lying in a simplex if we know the distances from the vertices?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Gy\\\"orgy P\\'al Geh\\'er","submitted_at":"2015-07-15T21:56:19Z","abstract_excerpt":"It is an elementary fact that if we fix an arbitrary set of $d+1$ affine independent points $\\{p_0,\\dots p_d\\}$ in $\\mathbb{R}^d$, then the Euclidean distances $\\{|x-p_j|\\}_{j=0}^d$ determine the point $x$ in $\\mathbb{R}^d$ uniquely. In this paper we investigate a similar problem in general normed spaces which is motivated by this known fact. Namely, we characterize those, at least $d$-dimensional, real normed spaces $(X, \\|\\cdot\\|)$ such that for every set of $d+1$ affine independent points $\\{p_0,\\dots p_d\\} \\subset X$, the distances $\\{\\|x-p_j\\|\\}_{j=0}^d$ determines the point $x$ lying in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05114","kind":"arxiv","version":2},"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"}