{"paper":{"title":"Mean Width of a Regular Simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.MG","authors_text":"Steven R. Finch","submitted_at":"2011-11-21T19:10:02Z","abstract_excerpt":"The mean width is a measure on n-dimensional convex bodies. An integral formula for the mean width of a regular n-simplex appeared in the electrical engineering literature in 1997. As a consequence, expressions for the expected range of a sample of n+1 normally distributed variables, for n<=6, carry over to widths of regular n-simplices. As another consequence, precise asymptotics for the mean width become available as n->infty."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4976","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"}