A093063 - OEIS

%I #16 Nov 21 2024 08:04:53

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

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

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

%N Decimal expansion of (2 + 4*sqrt(2) + (4 + sqrt(2))*arcsinh(1))/30.

%C Average length of a line picked at random inside an isosceles right triangle with legs of unit length.

%C Close but not equal to sqrt(2)-1 = 0.414213562.

%H G. C. Greubel, <a href="/A093063/b093063.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangleLinePicking.html">Triangle Line Picking</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 0.41429330259503377743084107857530325185642398130824894805...

%t RealDigits[(2+4Sqrt[2]+(4+Sqrt[2])ArcSinh[1])/30,10,120][[1]] (* _Harvey P. Dale_, Jan 20 2012 *)

%o (PARI) default(realprecision, 100); (2+4*sqrt(2)+(4+sqrt(2))*asinh(1))/30 \\ _G. C. Greubel_, Sep 27 2018

%o (Magma) SetDefaultRealField(RealField(100)); (2+4*Sqrt(2)+(4+Sqrt(2) )*Argsinh(1))/30; // _G. C. Greubel_, Sep 27 2018

%Y Cf. A093064.

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Mar 16 2004