A348681 Decimal expansion of the average length of a chord in a unit square defined by the intersection of the perimeter with a straight line passing through 2 points uniformly and independently chosen at random in the interior of the square.

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

Offset: 1

Author

Amiram Eldar, Oct 29 2021

Keywords

• nonn
• cons

Examples

			1.04281086632944135666196471321448794982806313555801...
		

References

• A. M. Mathai, An introduction to geometrical probability: distributional aspects with applications, Amsterdam: Gordon and Breach, 1999, p. 221, ex. 2.3.7.

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. A091505, A247674, A348680, A348682, A348683.

Programs

Mathematica

RealDigits[(2/3) * (Log[1 + Sqrt[2]] + (2 + Sqrt[2])/5), 10, 100][[1]]

PARI

(2/3) * (log(1 + sqrt(2)) + (2 + sqrt(2))/5) \\ Michel Marcus, Oct 29 2021

Formula

Equals (2/3) * (log(1 + sqrt(2)) + (2 + sqrt(2))/5).