A363966 Decimal expansion of the probability that a sphere that is passing through 4 points uniformly and independently chosen at random in a 3D ball is completely lying inside the ball.

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

Offset

0,2

Comments

The corresponding 2D probability, that a circle that is passing through 3 points uniformly and independently chosen at random in a 2D disk is completely lying inside the disk, is 2/5.

For the general solution in any number of dimensions see the solution of the user "joriki" in the Mathematics Stackexchange link.

Links

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

Thomas Browning, Probability of random sphere lying inside the unit ball, Mathematics Stackexchange, 2020.

Formula

Equals 24*Pi^2/1925.

Example

0.12304961331228291265040404363481954662209287572663...

Mathematica

RealDigits[24*Pi^2/1925, 10, 120][[1]]

Prog

(PARI) 24*Pi^2/1925

Crossrefs

Cf. A093591.

Sequence in context: A121598 A375417 A344276 * A258818 A261275 A140326

Adjacent sequences: A363963 A363964 A363965 * A363967 A363968 A363969

Keyword

nonn,cons

Author

Amiram Eldar, Jun 30 2023

Status

approved