A396274 Decimal expansion of the probability that the line segment connecting two points, chosen independently and uniformly at random in an annulus with a radii ratio of 1:2, lies entirely within the annulus.

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Jonathan K. Hodge, Emily Marshall, and Geoff Patterson, Gerrymandering and Convexity, The College Mathematics Journal, Vol. 41, No. 4 (2010), pp. 312-324.

Eric Weisstein's World of Mathematics, Convexity Coefficient.

Index entries for transcendental numbers.

Formula

Equals 8/9 - 2/(sqrt(3)*Pi).

Equals 8/9 - A165952.

Example

0.521336291941027522548004556680242594623964568644461...

Mathematica

RealDigits[8/9 - 2/(Sqrt[3]*Pi), 10, 120][[1]]

Prog

(PARI) 8/9 - 2/(sqrt(3)*Pi)

Crossrefs

Cf. A165952, A395391, A396275.

Sequence in context: A133615 A136161 A350688 * A197383 A348186 A356030

Adjacent sequences: A396271 A396272 A396273 * A396275 A396276 A396277

Keyword

nonn,cons

Author

Amiram Eldar, May 21 2026

Status

approved