A395214 Decimal expansion of the probability that the unique circle that passes through three points that are independently and uniformly selected at random in the interior of a cube is entirely contained in that cube.

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

Offset

0,1

Comments

The probability that the three points are collinear (i.e., lie on the same straight line) and do not define a circle is 0.

Links

Table of n, a(n) for n=0..104.

Fernando Affentranger, Random circles in the d-dimensional unit ball, Journal of Applied Probability , Vol. 26, No. 2 (1989), p. 408-412; JSTOR link.

Index entries for transcendental numbers.

Formula

Equals 12*Pi^2/245.

Example

0.4834091951553971568408730285653625045867934403546509...

Mathematica

RealDigits[12*Pi^2/245, 10, 120][[1]]

Prog

(PARI) 12*Pi^2/245

Crossrefs

Cf. A002388, A395207, A395208, A395209, A395210, A395211, A395212, A395213.

Sequence in context: A309217 A217602 A392243 * A300690 A193077 A271871

Adjacent sequences: A395211 A395212 A395213 * A395215 A395216 A395217

Keyword

nonn,cons

Author

Amiram Eldar, Apr 16 2026

Status

approved