{"paper":{"title":"On curves and polygons with the equiangular chord property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Serge Tabachnikov, Tarik Aougab, Xidian Sun, Yuwen Wang","submitted_at":"2013-11-04T19:16:36Z","abstract_excerpt":"Let $C$ be a smooth, convex curve on either the sphere $\\mathbb{S}^{2}$, the hyperbolic plane $\\mathbb{H}^{2}$ or the Euclidean plane $\\mathbb{E}^{2}$, with the following property: there exists $\\alpha$, and parameterizations $x(t), y(t)$ of $C$ such that for each $t$, the angle between the chord connecting $x(t)$ to $y(t)$ and $C$ is $\\alpha$ at both ends.\n  Assuming that $C$ is not a circle, E. Gutkin completely characterized the angles $\\alpha$ for which such a curve exists in the Euclidean case. We study the infinitesimal version of this problem in the context of the other two constant cur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0817","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"}