HackerPapers

arXiv:1912.06345math.NT

The Irrationality Measure of Pi is at most 7.103205334137...

Doron Zeilberger, Wadim Zudilin

Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.

Abstract

We use a variant of Salikhov's ingenious proof that the irrationality measure of $π$ is at most $7.606308\dots$ to prove that, in fact, it is at most $7.103205334137\dots$. Accompanying Maple package: While this article has a fully rigorous human-made and human-readable proof of the claim in the title, it was discovered thanks to the Maple package available from http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/pimeas.html

arXiv comments
13 pages; v2: Lemma 2 corrected; accompanying Maple package available from http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/pimeas.html
Journal reference
Moscow J. Comb. Number Th. 9 (2020) 407-419
DOI
doi:10.2140/moscow.2020.9.407
Subjects
math.NTNumber Theory math.CAClassical Analysis and ODEs math.COCombinatorics

On Hacker News

Linked by 1 identifiable commenter in 1 comment across 1 thread, from Jun 2022 to Jun 2022.

Comments linking this paper, per year.

Discussed in comments1 thread

  1. Even more pi in the sky: Calculating 100T digits of pi on Google Cloud 1 comment

    • Fun fact: Mahler famously showed that if p/q is a rational number then |\pi - p/q| > 1/q^42. So we can't have a string of 4242T zeros after first 101T digits :-) The exponent 42 has since been improved by a series of works to 7.1032 - https://arxiv.org/abs/1912.06345

      madarsView on HNParent context

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.