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

1,3

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

Table of n, a(n) for n=1..105.

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

Formula

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

Example

1.04281086632944135666196471321448794982806313555801...

Mathematica

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

Prog

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

Crossrefs

Cf. A091505, A247674, A348680, A348682, A348683.

Sequence in context: A199814 A195347 A200693 * A241298 A019953 A241005

Adjacent sequences: A348678 A348679 A348680 * A348682 A348683 A348684

Keyword

nonn,cons

Author

Amiram Eldar, Oct 29 2021

Status

approved