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Irrationality Measure of Pi

General Mathematics 2022-05-13 v9

Abstract

The first estimate of the upper bound μ(π)42\mu(\pi)\leq42 of the irrationality measure of the number π\pi was computed by Mahler in 1953, and more recently it was reduced to μ(π)7.6063\mu(\pi)\leq7.6063 by Salikhov in 2008. Here, it is shown that π\pi has the same irrationality measure μ(π)=μ(α)=2\mu(\pi)=\mu(\alpha)=2 as almost every irrational number α>0\alpha>0.

Keywords

Cite

@article{arxiv.1902.08817,
  title  = {Irrationality Measure of Pi},
  author = {N. A. Carella},
  journal= {arXiv preprint arXiv:1902.08817},
  year   = {2022}
}

Comments

Thirty Three Pages. Keywords: Irrational number; Irrationality measure; Circle number; Pi; Flint Hills series; Flat Hills series