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%I #21 Sep 12 2022 04:52:18
%S 3,1,4,1,5,3,3,3,3,8,7,0,5,0,9,4,6,1,8,6,3,6,3,9,8,2,2,1,9,6,4,6,2,4,
%T 0,7,1,1,9,9,1,2,4,1,7,9,2,1,3,3,6,3,2,6,4,2,4,2,9,4,0,2,1,3,5,9,2,0,
%U 5,0,8,9,0,0,7,4,0,5,8,4,0,4,5,1,5,1,0,1,0,0,8,9,6,3,0,5,8,4,7,5,8,4,0,7,2,1,6,7,9,5,7,0,9,7,8,9,3,1,9,7,7
%N Decimal expansion of sqrt(120-18*sqrt(3))/3.
%C An approximation for Pi, obtained by a geometrical construction by Kochański (1685). - _Amiram Eldar_, Sep 12 2022
%D Benjamin Bold, Famous Problems of Geometry and How to Solve Them, New York: Dover, 1982, p. 44.
%D J. L. Heilbron, Geometry Civilized: History, Culture, and Technique, Oxford University Press, 2000, pp. 250-252.
%D Hugo Steinhaus, Mathematical Snapshots, 3rd ed., New York: Dover, 1999, p. 143.
%H Mordechai Ben-Ari, <a href="https://doi.org/10.1007/978-3-031-13566-8">Mathematical Surprises</a>, Springer, 2022, p. 30.
%H Henryk Fukś, <a href="https://doi.org/10.1007/s00283-012-9312-1">Adam Adamandy Kochanski's approximations of Pi: reconstruction of the algorithm</a>, Math. Intelligencer, Vol. 34, No. 4 (2012), pp. 40-45; <a href="http://arxiv.org/abs/1111.1739">arXiv preprint</a>, arXiv:1111.1739 [math.HO], 2011-2014.
%H Adam Adamandy Kochański, <a href="https://archive.org/details/s1id13206510/page/394/mode/2up">Observationes Cyclometricae ad facilitandam Praxin accomodatae</a>, Acta Eruditorum, Vol. 4 (1685), pp. 394-398.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KochanskisApproximation.html">Kochanski's Approximation</a>.
%e 3.1415333387050946186363982219646240711991241792133632642429...
%t RealDigits[Sqrt[120 - 18*Sqrt[3]]/3, 10, 100][[1]] (* _Amiram Eldar_, Sep 12 2022 *)
%o (PARI) sqrt(40/3-2*sqrt(3)) \\ _Charles R Greathouse IV_, Mar 25 2014
%Y Cf. A199657, A199658, A199671, A199672.
%K nonn,cons
%O 1,1
%A _N. J. A. Sloane_, Jan 23 2013
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