{"paper":{"title":"Origami rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Joe Buhler, Ron Graham, Steve Butler, Warwick de Launey","submitted_at":"2010-11-11T21:06:35Z","abstract_excerpt":"Motivated by a question in origami, we consider sets of points in the complex plane constructed in the following way. Let $L_\\alpha(p)$ be the line in the complex plane through $p$ with angle $\\alpha$ (with respect to the real axis). Given a fixed collection $U$ of angles, let $\\RU$ be the points that can be obtained by starting with $0$ and $1$, and then recursively adding intersection points of the form $L_\\alpha(p) \\cap L_\\beta(q)$, where $p, q$ have been constructed already, and $\\alpha, \\beta$ are distinct angles in $U$.\n  Our main result is that if $U$ is a group with at least three elem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2769","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"}