{"paper":{"title":"A set of the Vi\\`ete-like recurrence relations for the unity constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"B. M. Quine, S. M. Abrarov","submitted_at":"2017-02-03T03:36:29Z","abstract_excerpt":"Using a simple Vi\\`ete-like formula for $\\pi$ based on the nested radicals $a_k = \\sqrt{2 + a_{k-1}}$ and $a_1 = \\sqrt{2}$, we derive a set of the recurrence relations for the constant $1$. Computational test shows that application of this set of the Vi\\`ete-like recurrence relations results in a rapid convergence to unity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00901","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"}