This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A361601 #9 Feb 10 2025 08:44:47 %S A361601 1,0,9,6,0,5,6,8,1,5,2,4,0,6,2,5,4,8,9,0,6,1,7,2,6,5,6,5,6,4,1,2,5,7, %T A361601 3,5,6,9,5,9,4,2,4,7,2,7,3,1,8,4,0,8,6,3,3,9,9,1,0,9,6,8,7,7,7,2,0,6, %U A361601 7,8,8,7,1,0,9,2,9,7,0,9,1,0,7,7,9,8,7,0,6,3,1,4,8,8,8,2,5,7,5,7,5,7,6,9,1 %N A361601 Decimal expansion of the maximum possible disorientation angle between two identical cubes (in radians). %C A361601 Mackenzie and Thomson (1957) attributed the idea of finding this angle to the British theoretical physicist Frederick Charles Frank (1911-1988), who proposed this problem in 1949. %C A361601 The disorientation angle between two identical bodies is the least angle of rotation about an axis through the center of mass of one of the bodies that is needed to bring it into the same orientation as the other body. For two cubes with indistinguishable faces, there are 24 rotations angles that will bring the first cube into coincidence with the second, and the disorientation angle is the least of them. %C A361601 The rotation which achieves this maximum disorientation can be described as a rotation by 90 degrees about any axis parallel to a face diagonal of the cube. %C A361601 The angle in degrees is 62.7994296198... %C A361601 The solution to the analogous two-dimensional problem with two squares is the trivial value Pi/4 (A003881). %H A361601 D. C. Handscomb, <a href="https://doi.org/10.4153/CJM-1958-010-0">On the random disorientation of two cubes</a>, Canadian Journal of Mathematics, Vol. 10 (1958), pp. 85-88. %H A361601 J. K. Mackenzie, <a href="http://www.jstor.org/stable/2333059">Second Paper on Statistics Associated with the Random Disorientation of Cubes</a>, Biometrika, Vol. 45, No. 1-2 (1958), pp. 229-240. %H A361601 J. K. Mackenzie and M. J. Thomson, <a href="http://www.jstor.org/stable/2333253">Some Statistics Associated with the Random Disorientation of Cubes</a>, Biometrika, Vol. 44, No. 1-2 (1957), pp. 205-210. %H A361601 Wikipedia, <a href="https://en.wikipedia.org/wiki/Misorientation">Misorientation</a>. %H A361601 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>. %F A361601 Equals arccos(sqrt(2)/2 - 1/4). %F A361601 Equals 2 * arccos(1/2 + sqrt(2)/4). %F A361601 Equals 2 * arctan((sqrt(2)-1) * sqrt(5-2*sqrt(2))). %e A361601 1.09605681524062548906172656564125735695942472731840... %t A361601 RealDigits[ArcCos[Sqrt[2]/2 - 1/4], 10, 100][[1]] %o A361601 (PARI) acos(sqrt(2)/2 - 1/4) %Y A361601 Cf. A003881, A201488, A361602, A361603, A361604. %K A361601 nonn,cons %O A361601 1,3 %A A361601 _Amiram Eldar_, Mar 17 2023