

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
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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 18771896, 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. 36.
John E. Zimmerman, Enoch Beery Seitz 18461883.


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



