{"paper":{"title":"Fermat's spiral and the line between Yin and Yang","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Oleg Verbitsky, Taras Banakh, Yaroslav Vorobets","submitted_at":"2009-02-09T22:57:49Z","abstract_excerpt":"Let $D$ denote a disk of unit area. We call a subset $A$ of $D$ perfect if it has measure 1/2 and, with respect to any axial symmetry of $D$, the maximal symmetric subset of $A$ has measure 1/4. We call a curve $\\beta$ in $D$ an yin-yang line if\n  $\\beta$ splits $D$ into two congruent perfect sets,\n  $\\beta$ crosses each concentric circle of $D$ twice,\n  $\\beta$ crosses each radius of $D$ once.\n  We prove that Fermat's spiral is a unique yin-yang line in the class of smooth curves algebraic in polar coordinates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1556","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"}