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A228496 Decimal expansion of arccos(2/3). 0
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

LINKS

Table of n, a(n) for n=0..81.

emc2, Bille glissant sur une sphère (in French).

V. Jayanth, C. Raghunandan, 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

FORMULA

Equals arcsin(sqrt(5)/3).

EXAMPLE

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

MAPLE

evalf(arccos(2/3)) ;

PROG

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

CROSSREFS

Sequence in context: A049255 A028577 A039662 * A259616 A247036 A202320

Adjacent sequences:  A228493 A228494 A228495 * A228497 A228498 A228499

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Aug 23 2013

STATUS

approved

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Last modified February 26 14:39 EST 2021. Contains 341632 sequences. (Running on oeis4.)