cp's OEIS Frontend

A228496 Decimal expansion of arccos(2/3).

%I A228496 #35 Nov 21 2024 07:47:27
%S A228496 8,4,1,0,6,8,6,7,0,5,6,7,9,3,0,2,5,5,7,7,6,5,2,5,0,3,1,8,2,6,4,3,0,7,
%T A228496 4,6,7,0,2,0,7,8,7,8,5,6,3,9,8,3,9,2,1,9,7,7,8,5,2,2,8,0,4,6,9,2,0,8,
%U A228496 9,3,0,3,4,7,6,3,3,7,3,6,0,5
%N A228496 Decimal expansion of arccos(2/3).
%C A228496 The value describes the smaller of the internal angles in the triangle of the surfaces of the Tetrakis Hexahedron.
%C A228496 The value equals Pi/2 minus A156547, the 90-degree complement to 41.81031... degrees.
%C A228496 The value is a little bit larger than the 4th root of 1/2, which is 0.8408964... = A228497.
%C A228496 If a ball assimilated to a point rolls without friction on a sphere starting from the top with zero initial velocity, this value is the angle in radians, measured at the center of the sphere, from the top of the sphere to the point at which the ball leaves the surface of the sphere. See Jayanth et al. - _Robert FERREOL_, Sep 14 2019
%C A228496 The maximum possible value of the least of the nine acute angles between pairs of edges of two randomly disoriented cubes (in radians, see A361618). - _Amiram Eldar_, Mar 18 2023
%H A228496 emc2, <a href="http://e.m.c.2.free.fr/boule-sur-sphere.htm">Bille glissant sur une sphère</a> (in French).
%H A228496 V. Jayanth, C. Raghunandan and Anindya Kumar Biswas, <a href="https://arxiv.org/abs/0808.3531">A sphere moving down the surface of a static sphere and a simple phase diagram</a>, arXiv:0808.3531 [physics.class-ph], 2008-2009.
%H A228496 R. J. Mathar, <a href="http://arxiv.org/abs/1309.3705">Hierarchical Subdivision of the Simple Cubic Lattice</a>, arXiv preprint arXiv:1309.3705 [math.MG], 2013.
%H A228496 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetrakis_hexahedron">Tetrakis hexahedron</a>.
%H A228496 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A228496 Equals arcsin(sqrt(5)/3).
%F A228496 Equals arctan(sqrt(5)/2). - _Amiram Eldar_, May 24 2021
%e A228496 Equals 0.8410686705679302557765... radians  = 48.189685... degrees.
%p A228496 evalf(arccos(2/3)) ;
%t A228496 RealDigits[ArcCos[2/3], 10, 100][[1]] (* _Amiram Eldar_, May 24 2021 *)
%o A228496 (PARI) acos(2/3) \\ _Michel Marcus_, Sep 14 2019
%Y A228496 Cf. A156547, A228497, A361618.
%K A228496 cons,nonn
%O A228496 0,1
%A A228496 _R. J. Mathar_, Aug 23 2013