A301865 Decimal expansion of the probability that 2 planes, each passes through 3 random points inside a sphere, will intersect within the sphere.

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

Offset

1,1

Comments

The problem was proposed and solved by Enoch Beery Seitz in 1883.

References

Stanley Rabinowitz, Problems and Solutions from the Mathematical Visitor 1877-1896, MathPro Press, 1991, pp. 173-174.

Links

Table of n, a(n) for n=1..87.

Enoch Beery Seitz, Problem 215, The Mathematical Visitor, Vol. 2, No. 3 (1883), p. 58-59.

Formula

(63/64)^4*(5*Pi/16)^2

Example

0.90498647894587498063636944964469884094259718856766...

Mathematica

RealDigits[(63/64)^4*(5*Pi/16)^2, 10, 100][[1]]

Prog

(PARI) (63/64)^4*(5*Pi/16)^2 \\ Altug Alkan, Mar 28 2018

Crossrefs

Cf. A301862, A301863, A301864.

Sequence in context: A196398 A192932 A361061 * A309605 A010770 A021921

Adjacent sequences: A301862 A301863 A301864 * A301866 A301867 A301868

Keyword

nonn,cons

Author

Amiram Eldar, Mar 28 2018

Status

approved