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%I #20 Jan 17 2018 03:23:35
%S 4,2,2,1,5,7,7,3,3,1,1,5,8,2,6,6,2,7,0,2,3,3,6,5,9,1,6,6,2,3,8,5,0,7,
%T 5,8,1,2,3,4,0,7,9,7,0,6,9,7,6,2,9,0,4,3,9,3,5,7,3,7,5,9,5,0,8,6,5,7,
%U 8,7,4,6,9,8,3,8,5,5,4,9,6,3,7,7,9,0,7,9,8,1,6,7,4,2,4,4,6,9,0,1,1,4
%N Decimal expansion of volume of the Reuleaux tetrahedron.
%H Vincenzo Librandi, <a href="/A102888/b102888.txt">Table of n, a(n) for n = 0..5000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DefiniteIntegral.html">Definite Integral</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ReuleauxTetrahedron.html">Reuleaux Tetrahedron</a>
%F (8/3)*Pi - (27/4)*arccos(1/3) + sqrt(2)/4
%F = (3*sqrt(2) - 49*Pi + 162*arctan(sqrt(2)))/12
%F = (1/24)*(6*sqrt(2) + 16*Pi + 57*arccos(17/81) - 132*arctan(sqrt(2))).
%e 0.422157733...
%t RealDigits[8 Pi/3 - 27 ArcSec[3]/4 + Sqrt[2]/4, 10, 102][[1]] (* _Eric W. Weisstein_, Dec 15 2017 *)
%o (PARI) 8/3*Pi - (27/4)*acos(1/3) + sqrt(2)/4 \\ _Michel Marcus_, Dec 15 2017
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Jan 16 2005
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