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Decimal expansion of bean curve area.
1

%I #23 Feb 09 2018 15:50:25

%S 1,0,5,8,0,4,9,6,2,9,1,3,6,6,2,7,0,7,9,5,1,3,2,1,2,3,1,6,9,5,7,9,2,4,

%T 1,7,7,1,6,5,7,0,5,3,1,1,3,8,7,4,3,2,0,0,2,4,1,5,7,6,6,2,1,2,3,0,9,7,

%U 3,8,5,2,2,3,2,3,7,0,6,4,3,2,1,4,9,0,7,2,9,0,9,7,9,0,3,6,8,4,3,1,8,3,2,7,9

%N Decimal expansion of bean curve area.

%C area = 7*Pi/(12*sqrt(3)). - _Eric W. Weisstein_, Feb 05 2018

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeanCurve.html">Bean Curve</a>

%e 1.058049629...

%t area = Sqrt[2] NIntegrate[Sqrt[x (1 - x + Sqrt[1 + (2 - 3 x) x])], {x, 0, 1}, WorkingPrecision -> 120]; Take[RealDigits[area][[1]], 105]

%t RealDigits[7 Pi/(12 Sqrt[3]), 10, 105][[1]] (* _Eric W. Weisstein_, Feb 05 2018 *)

%Y Cf. A193306 (arc length).

%K nonn,cons,easy

%O 1,3

%A _Jean-François Alcover_, Jul 29 2011