{"paper":{"title":"How large dimension guarantees a given angle?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Andr\\'as M\\'ath\\'e, Bal\\'azs Strenner, Gergely Kiss, Pertti Mattila, P\\'eter Maga, Tam\\'as Keleti, Viktor Harangi","submitted_at":"2011-01-07T12:55:19Z","abstract_excerpt":"We study the following two problems:\n  (1) Given $n\\ge 2$ and $\\al$, how large Hausdorff dimension can a compact set $A\\su\\Rn$ have if $A$ does not contain three points that form an angle $\\al$?\n  (2) Given $\\al$ and $\\de$, how large Hausdorff dimension can a %compact subset $A$ of a Euclidean space have if $A$ does not contain three points that form an angle in the $\\de$-neighborhood of $\\al$?\n  An interesting phenomenon is that different angles show different behaviour in the above problems. Apart from the clearly special extreme angles 0 and $180^\\circ$, the angles $60^\\circ,90^\\circ$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1426","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"}