A300284 Decimal expansion of the probability that a bullet, shot randomly at a cube that is thrown into the air, will pass through the opposite side.

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

Offset

0,2

Comments

The solution to the problem proposed and solved by Enoch Beery Seitz in 1882: "A cube is thrown into the air and a random shot fired through it; find the chance that the shot passes through the opposite side."

The corresponding probability for the 2D case is 1/2 - log(2)/Pi = 0.279364...

References

Stanley Rabinowitz, Problems and Solutions from the Mathematical Visitor 1877-1896, MathPro Press, 1991, page 26.

Links

Table of n, a(n) for n=0..86.

Enoch Beery Seitz, Problem 201, The Mathematical Visitor, Vol. 2, No. 1 (1882), p. 21.

Benjamin Franklin Finkel, A Mathematical Solution Book, Kidder, Mo., Kibley, Cokely & Co., 1888, page 349.

Benjamin Franklin Finkel, Biography: E. B. Seitz, The American Mathematical Monthly, Vol. 1, No. 1 (1894), pp. 3-6.

John E. Zimmerman, Enoch Beery Seitz 1846-1883.

Formula

Equals ((4*sqrt(2)*arctan(1/sqrt(2)) + log(4/3) - Pi)/Pi.

Example

0.1998248956983873830415992511930687281182397696903038715831268954549617964416...

Mathematica

RealDigits[(4*Sqrt[2]*ArcTan[1/Sqrt[2]]+Log[4/3]-Pi)/Pi, 10, 100][[1]]

Crossrefs

Sequence in context: A292825 A347058 A091667 * A347057 A334446 A051554

Adjacent sequences: A300281 A300282 A300283 * A300285 A300286 A300287

Keyword

nonn,cons

Author

Amiram Eldar, Mar 01 2018

Extensions

Offset corrected by Amiram Eldar, Apr 24 2021

Status

approved