{"paper":{"title":"The irrationality measure of $\\pi$ as seen through the eyes of $\\cos(n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Erin P. J. Pearse, Sully F. Chen","submitted_at":"2018-07-09T06:20:51Z","abstract_excerpt":"For different values of $\\gamma \\geq 0$, analysis of the end behavior of the sequence $a_n = \\cos (n)^{n^\\gamma}$ yields a strong connection to the irrationality measure of $\\pi$. We show that if $\\limsup |\\cos n|^{n^2} \\neq 1$, then the irrationality measure of $\\pi$ is exactly 2. We also give some numerical evidence to support the conjecture that $\\mu(\\pi)=2$, based on the appearance of some startling subsequences of $\\cos(n)^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02955","kind":"arxiv","version":3},"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"}