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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. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified December 4 23:46 EST 2022. Contains 358572 sequences. (Running on oeis4.)