A228496 Decimal expansion of arccos(2/3).

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, 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, 9, 3, 0, 3, 4, 7, 6, 3, 3, 7, 3, 6, 0, 5

Offset: 0

Author

R. J. Mathar, Aug 23 2013

Keywords

• cons
• nonn

Comments

The value describes the smaller of the internal angles in the triangle of the surfaces of the Tetrakis Hexahedron.

The value equals Pi/2 minus A156547, the 90-degree complement to 41.81031... degrees.

The value is a little bit larger than the 4th root of 1/2, which is 0.8408964... = A228497.

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

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

Examples

			Equals 0.8410686705679302557765... radians  = 48.189685... degrees.
		

Links

• emc2, Bille glissant sur une sphère (in French).
• V. Jayanth, C. Raghunandan and Anindya Kumar Biswas, A sphere moving down the surface of a static sphere and a simple phase diagram, arXiv:0808.3531 [physics.class-ph], 2008-2009.
• R. J. Mathar, Hierarchical Subdivision of the Simple Cubic Lattice, arXiv preprint arXiv:1309.3705 [math.MG], 2013.
• Wikipedia, Tetrakis hexahedron.
• Index entries for transcendental numbers

Crossrefs

Cf. A156547, A228497, A361618.

Programs

Maple

evalf(arccos(2/3)) ;

Mathematica

RealDigits[ArcCos[2/3], 10, 100][[1]] (* Amiram Eldar, May 24 2021 *)

PARI

acos(2/3) \\ Michel Marcus, Sep 14 2019

Formula

Equals arcsin(sqrt(5)/3).

Equals arctan(sqrt(5)/2). - Amiram Eldar, May 24 2021