{"paper":{"title":"Efficient computation of pi by the Newton - Raphson iteration and a two-term Machin-like formula","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":"2017-12-12T18:11:34Z","abstract_excerpt":"In our recent publication we have proposed a new methodology for determination of the two-term Machin-like formula for pi with small arguments of the arctangent function of kind $$ \\frac{\\pi }{4} = {2^{k - 1}}\\arctan \\left( {\\frac{1}{{{\\beta_1}}}} \\right) + \\arctan \\left( {\\frac{1}{{{\\beta_2}}}} \\right), $$ where $k$ and ${\\beta_1}$ are some integers and ${\\beta_2}$ is a rational number, dependent upon ${\\beta_1}$ and $k$. Although ${1/\\left|\\beta_2\\right|}$ may be significantly smaller than ${1/\\beta_1}$, the large numbers in the numerator and denominator of $\\beta_2$ decelerate the computati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04414","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"}