{"paper":{"title":"A Geometric Structure Associated with the Convex Polygon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Kai Jin","submitted_at":"2015-12-12T09:31:22Z","abstract_excerpt":"We propose a geometric structure induced by any given convex polygon $P$, called $Nest(P)$, which is an arrangement of $\\Theta(n^2)$ line segments, each of which is parallel to an edge of $P$, where $n$ denotes the number of edges of $P$. We then deduce six nontrivial properties of $Nest(P)$ from the convexity of $P$ and the parallelism of the line segments in $Nest(P)$. Among others, we show that $Nest(P)$ is a subdivision of the exterior of $P$, and its inner boundary interleaves the boundary of $P$. They manifest that $Nest(P)$ has a surprisingly good interaction with the boundary of $P$. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03897","kind":"arxiv","version":11},"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"}