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A361619
Decimal expansion of the standard deviation of the distribution of the least of the nine acute angles between pairs of edges of two randomly disoriented cubes (in radians).
4
1, 7, 9, 9, 7, 3, 0, 7, 2, 2, 8, 8, 5, 8, 0, 1, 2, 3
OFFSET
0,2
COMMENTS
The corresponding value in degrees is 10.3116974681...
LINKS
J. K. Mackenzie, Second Paper on Statistics Associated with the Random Disorientation of Cubes, Biometrika, Vol. 45, No. 1-2 (1958), pp. 229-240.
J. K. Mackenzie and M. J. Thomson, Some Statistics Associated with the Random Disorientation of Cubes, Biometrika, Vol. 44, No. 1-2 (1957), pp. 205-210.
Wikipedia, Misorientation.
FORMULA
Equals sqrt(<t^2> - <t>^2), where <t^k> = Integral_{t=0..arccos(2/3)} t^k * P(t) dt, and P(t) is given in A361618.
EXAMPLE
0.179973072288580123...
MATHEMATICA
See the program in the links section.
CROSSREFS
KEYWORD
nonn,cons,more
AUTHOR
Amiram Eldar, Mar 18 2023
STATUS
approved