{"paper":{"title":"A Note on the Size of the Largest Ball Inside a Convex Polytope","license":"","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Imre Barany, Nandor Simanyi","submitted_at":"2005-05-14T06:45:42Z","abstract_excerpt":"Let $m>1$ be an integer, $B_m$ the set of all unit vectors of $\\Bbb R^m$ pointing in the direction of a nonzero integer vector of the cube $[-1, 1]^m$. Denote by $s_m$ the radius of the largest ball contained in the convex hull of $B_m$. We determine the exact value of $s_m$ and obtain the asymptotic equality $s_m\\sim\\frac{2}{\\sqrt{\\log m}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505301","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"}