{"paper":{"title":"A formula for pi involving nested radicals","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":"2016-10-25T02:39:56Z","abstract_excerpt":"We present a new formula for pi involving nested radicals with rapid convergence. This formula is based on the arctangent function identity with argument $x=\\sqrt{2-{{a}_{k-1}}}/{{a}_{k}}$, where \\[ {{a}_{k}}=\\underbrace{\\sqrt{2+\\sqrt{2+\\sqrt{2+\\cdots +\\sqrt{2}}}}}_{k\\,\\,\\text{square}\\,\\,\\text{roots}} \\] is a nested radical consisting of $k$ square roots. The computational test we performed reveals that the proposed formula for pi provides a significant improvement in accuracy as the integer $k$ increases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07713","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"}