A093063 Decimal expansion of (2 + 4*sqrt(2) + (4 + sqrt(2))*arcsinh(1))/30.

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, 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, 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

Offset: 0

Author

Eric W. Weisstein, Mar 16 2004

Keywords

• nonn
• cons

Comments

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

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

Examples

			0.41429330259503377743084107857530325185642398130824894805...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Triangle Line Picking
• Index entries for transcendental numbers

Crossrefs

Cf. A093064.

Programs

Magma

SetDefaultRealField(RealField(100)); (2+4*Sqrt(2)+(4+Sqrt(2) )*Argsinh(1))/30; // G. C. Greubel, Sep 27 2018

Mathematica

RealDigits[(2+4Sqrt[2]+(4+Sqrt[2])ArcSinh[1])/30,10,120][[1]] (* Harvey P. Dale, Jan 20 2012 *)

PARI

default(realprecision, 100); (2+4*sqrt(2)+(4+sqrt(2))*asinh(1))/30 \\ G. C. Greubel, Sep 27 2018