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
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
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 01 2018
EXTENSIONS
Offset corrected by Amiram Eldar, Apr 24 2021
STATUS
approved