{"paper":{"title":"Geometric constructibility of polygons lying on a circular arc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.AG","authors_text":"Delbrin Ahmed, Eszter K. Horv\\'ath, G\\'abor Cz\\'edli","submitted_at":"2017-10-24T15:54:07Z","abstract_excerpt":"For a positive integer $n$, an $n$-sided polygon lying on a circular arc or, shortly, an $n$-fan is a sequence of $n+1$ points on a circle going counterclockwise such that the \"total rotation\" $\\delta$ from the first point to the last one is at most $2\\pi$. We prove that for $n\\geq 3$, the $n$-fan cannot be constructed with straightedge and compass in general from its central angle $\\delta$ and its central distances, which are the distances of the edges from the center of the circle. Also, we prove that for each fixed $\\delta$ in the interval $(0, 2\\pi]$ and for every $n\\geq 5$, there exists a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08859","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"}