{"paper":{"title":"On Optimal Disc Covers and a New Characterization of the Steiner Center","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alfred M. Bruckstein, Yael Yankelevsky","submitted_at":"2013-12-01T15:18:17Z","abstract_excerpt":"Given N points in the plane $P_1 P_2...P_N$ and a location $\\Omega$, the union of discs with diameters $[\\Omega P_i], i = 1, 2,...N$ covers the convex hull of the points. The location $\\Omega_s$ minimizing the area covered by the union of discs, is shown to be the Steiner center of the convex hull of the points. Similar results for $d$-dimensional Euclidean space are conjectured."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0233","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"}