{"paper":{"title":"Approximate embedding of large polygons into $Z^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Michael Boshernitzan","submitted_at":"2012-08-05T15:49:43Z","abstract_excerpt":"Let $Z^2$ denote the standard lattice in the plane $R^2$. We prove that given a finite subset $S\\subset R^2$ and $\\eps>0$, then for all sufficiently large dilations $t>0$ there exists a rotation $\\rho\\colon R^2\\to R^2$ around the origin such that $\\dist(\\rho(tz),Z^2)<\\eps$, for all $z\\in S$. The result, in a larger generality, has been proved in 2006 by Tamar Ziegler (improving earlier results by Furstenberg, Katznelson, Weiss). The proof presented in the paper is short and self-contained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1026","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"}