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).

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

Offset: 0

Author

Amiram Eldar, Mar 18 2023

Keywords

• nonn
• cons
• more

Comments

The corresponding value in degrees is 10.3116974681...

Examples

			0.179973072288580123...
		

Links

• Amiram Eldar, Mathematica code for A361618 and A361619.
• 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.

Crossrefs

Cf. A228496, A361601, A361618, A361620, A361621.

Programs

Mathematica

(* See the program in the links section. *)

Formula

Equals sqrt( - ^2), where = Integral_{t=0..arccos(2/3)} t^k * P(t) dt, and P(t) is given in A361618.