A348683 Decimal expansion of the average length of a chord in a unit cube defined by the intersection of the surface with a straight line passing through 2 points uniformly and independently chosen at random in the interior of the cube.

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

Offset: 1

Author

Amiram Eldar, Oct 29 2021

Keywords

• nonn
• cons

Examples

			1.10284530377862705859305188874735596957733355965158...
		

Links

• Rodney Coleman, Random paths through convex bodies, Journal of Applied Probability, Vol. 6, No. 2 (1969), pp. 430-441; alternative link; author's link.

Crossrefs

Cf. A073012, A093066, A348680, A348681, A348682.

Programs

Mathematica

RealDigits[4/63 - Pi/9 + 17*Sqrt[2]/63 - 2*Sqrt[3]/21 + Log[1+Sqrt[2]]/3 + 2*Log[2+Sqrt[3]]/3, 10, 100][[1]]

PARI

4/63 - Pi/9 + 17*sqrt(2)/63 - 2*sqrt(3)/21 + log(1+sqrt(2))/3 + 2*log(2+sqrt(3))/3 \\ Michel Marcus, Oct 29 2021

Formula

Equals 4/63 - Pi/9 + 17*sqrt(2)/63 - 2*sqrt(3)/21 + log(1+sqrt(2))/3 + 2*log(2+sqrt(3))/3.