Geodesic
Reprint: On the approximation of $\pi$ (1953)
Documenta mathematica, Mahler Selecta (2019), pp. 557-570.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The aim of this paper is to determine an explicit lower bound, free of unknown constants, for the distance of $\pi$ from a given rational or algebraic number. In particular, Mahler proves that, for all positive integers $p,q\ge 2$, \par
$ \par \par \left|\pi-\frac{p}{q}\right|>\frac{1}{q^{42}}. \par \par $
\par Reprint of the author's paper [Nederl. Akad. Wet., Proc., Ser. A 56 (Indag. Math. 15), 30--42 (1953; Zbl 0053.36105)].
Classification : 11-03, 11J81 
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     author = {Mahler, Kurt},
     title = {Reprint: {On} the approximation of \(\pi\) (1953)},
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     volume = {Mahler Selecta},
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Mahler, Kurt. Reprint: On the approximation of \(\pi\) (1953). Documenta mathematica, Mahler Selecta (2019), pp. 557-570. http://geodesic.mathdoc.fr/item/DOCMA_2019__S1__a30/