A245699 Decimal expansion of the expected distance from a randomly selected point in a 45-45-90 degree triangle of base length 1 to the vertex of the right angle: (4+sqrt(2)*log(3+2*sqrt(2)))/12.
5, 4, 1, 0, 7, 5, 0, 8, 0, 0, 4, 6, 7, 4, 3, 5, 0, 4, 4, 6, 4, 6, 7, 3, 3, 6, 0, 0, 8, 3, 5, 2, 2, 6, 6, 7, 5, 5, 0, 2, 3, 1, 7, 7, 0, 7, 8, 2, 1, 8, 9, 0, 8, 4, 2, 9, 9, 5, 7, 1, 5, 9, 2, 0, 3, 2, 0, 5, 6, 6, 6, 8, 1, 8, 2, 3, 3, 8, 0, 6, 0, 1, 5, 5, 8, 8, 9, 6, 9, 1, 0, 7, 8, 5, 4, 2, 2, 0, 9, 3, 5, 6, 5, 2, 7, 8, 8, 4, 0, 3, 0, 4, 7, 4, 2, 3, 1, 8, 1, 4
Offset: 0
Examples
0.54107508004674350446467336008352266755023177078218908429957159203205...
Links
Crossrefs
Cf. A103712.
Programs
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Magma
SetDefaultRealField(RealField(100)); (4+Sqrt(2)*Log(3 +2*Sqrt(2)))/12; // G. C. Greubel, Oct 06 2018
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Maple
evalf((4+sqrt(2)*log(3+2*sqrt(2)))/12,100); # Muniru A Asiru, Oct 07 2018
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Mathematica
RealDigits[(4 + Sqrt[2]*Log[3 + 2*Sqrt[2]])/12, 10, 100][[1]] (* G. C. Greubel, Oct 06 2018 *)
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PARI
default(realprecision, 100); (4+sqrt(2)*log(3+2*sqrt(2)))/12 \\ G. C. Greubel, Oct 06 2018
Formula
Equals Integral_{y = 0..Pi/4; x = 0..1/(sqrt(2)*cos(y))} 4x^2 dx dy.
Equals Integral_{y = 0..Pi/4} (sqrt(2)/3)*sec^3(y) dy.