{"paper":{"title":"Why is Helfenstein's claim about equichordal points false?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Marek Rychlik","submitted_at":"2012-02-08T06:52:21Z","abstract_excerpt":"This article explains why a paper by Heinz G. Helfenstein entitled \"Ovals with equichordal points\", published in J.London Math.Soc.31, 54-57, 1956, is incorrect. We point out a  computational error which renders his conclusions invalid. More importantly, we explain that the method cannot be used to solve the equichordal point problem with the method presented there. Today, there is a solution to the problem: Marek R. Rychlik, \"A complete  solution to the equichordal point problem of Fujiwara, Blaschke, Rothe and Weizenb\\\"ock\", Inventiones Mathematicae 129 (1), 141-212, 1997. However, some math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1609","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"}