{"paper":{"title":"Approximating a convex body by a polytope using the epsilon-net theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"M\\'arton Nasz\\'odi","submitted_at":"2017-05-22T14:01:26Z","abstract_excerpt":"Giving a joint generalization of a result of Brazitikos, Chasapis and Hioni and results of Giannopoulos and Milman, we prove that roughly $\\left\\lceil \\frac{d}{(1-\\vartheta)^d}\\ln\\frac{1}{(1-\\vartheta)^d} \\right\\rceil$ points chosen uniformly and independently from a centered convex body $K$ in ${\\mathbb R}^d$ yield a polytope $P$ for which $\\vartheta K\\subseteq P\\subseteq K$ holds with large probability. The proof is simple, and relies on a combinatorial tool, the $\\varepsilon$-net theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07754","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"}