A130203 -id:A130203 - cp's OEIS frontend

A130204 Decimal expansion of the mean distance between two points picked at random in a quarter-disk.

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

Offset: 0

Eric W. Weisstein, May 16 2007

			0.47387726224232582979...

Eric Weisstein's World of Mathematics, Circular Sector Line Picking.

Cf. A093070, A130203.

RealDigits[32*(3 - 94*Sqrt[2] + 48*Pi + 6*Log[2*(Sqrt[2]-1)])/(135*Pi^2), 10, 100][[1]] (* Amiram Eldar, Jun 25 2021 *)

(32*(3 - 94*sqrt(2) + 48*Pi + 6*log(-2 + 2*sqrt(2))))/(135*Pi^2) \\ Michel Marcus, Jun 25 2021

Equals (32*(3 - 94*sqrt(2) + 48*Pi + 6*log(-2 + 2*sqrt(2))))/(135*Pi^2).

A307029 Decimal expansion of the average distance of a point from a line that passes through another 2 points, when the 3 points are randomly selected within a unit-radius disk.

Original entry on oeis.org

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

Offset: 0

Amiram Eldar, Mar 20 2019

			0.526998816760654618202070198485135757399687036263519...

Roger Pinkham, Problem 10585, The American Mathematical Monthly, Vol. 104, No. 5 (1997), pp. 456, solution, by Richard Holzsager, Vol. 106, No. 2 (1999), pp. 171-172.

Cf. A093070, A130203, A130204, A245684.

RealDigits[8192/(1575*Pi^2), 10, 100][[1]]

Equals 8192/(1575*Pi^2).

cp's OEIS Frontend

A130204 Decimal expansion of the mean distance between two points picked at random in a quarter-disk.

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