{"paper":{"title":"The Rational Distance Problem for Isosceles Triangles with one rational side","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Antoine Karam, Roy Barbara","submitted_at":"2013-01-21T17:25:04Z","abstract_excerpt":"For a triangle $\\Delta$, let (P) denote the problem of the existence of points in the plane of $\\Delta$, that are at rational distance to the 3 vertices of $\\Delta$. Answer to (P) is known to be positive in the following situation: $\\Delta$ has one rational side and the square of all sides are rational. Further, the set of solution-points is dense in the plane of $\\Delta$. See [3] The reader can convince himself that the rationality of one side is a reasonable minimum condition to set out, otherwise problem (P) would stay somewhat hazy and scattered. Now, even with the assumption of one ration"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4931","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"}