

A195696


Decimal expansion of arccos(sqrt(1/3)) and of arcsin(sqrt(2/3)) and arctan(sqrt(2)).


11



9, 5, 5, 3, 1, 6, 6, 1, 8, 1, 2, 4, 5, 0, 9, 2, 7, 8, 1, 6, 3, 8, 5, 7, 1, 0, 2, 5, 1, 5, 7, 5, 7, 7, 5, 4, 2, 4, 3, 4, 1, 4, 6, 9, 5, 0, 1, 0, 0, 0, 5, 4, 9, 0, 9, 5, 9, 6, 9, 8, 1, 2, 9, 3, 2, 1, 9, 1, 2, 0, 4, 5, 9, 0, 3, 9, 7, 6, 4, 5, 5, 3, 8, 7, 3, 9, 1, 6, 0, 2, 5, 8, 5, 6, 2, 8, 0, 7, 3, 4
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OFFSET

0,1


COMMENTS

Angle (in radians) between an edge and (the normal of) a face of the regular tetrahedron.  R. J. Mathar, Feb 23 2012
Also known as magic angle; root of P_2(cos(theta)), with P_2(x) being secondorder Legendre polynomial.  Stanislav Sykora, May 25 2012
From Stanislav Sykora, Nov 14 2013: (Start)
Also the angle between the body diagonal of a cube and an incident edge, and therefore the polar angle of the cone circumscribed to a cube from one of its vertices.
Also half of the tetrahedral angle (A156546).
In nuclear magnetic resonance, the angle, with respect to the direction of the main magnetic field, under which a solid sample needs to be spun in order to average to zero unwanted dipoledipole spin interactions (the magic angle spinning, or MAS, technique). (end)


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 53.
Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author]
Wikipedia, Tetrahedron
Wikipedia, Magic angle


EXAMPLE

arccos(sqrt(1/3)) =0.9553166181245092781638571025157577... = 54.73561031... deg


MATHEMATICA

See A195695.
RealDigits[ArcTan[Sqrt[2]], 10, 120][[1]] (* Harvey P. Dale, Dec 13 2014 *)


PROG

(PARI) atan(sqrt(2)) \\ G. C. Greubel, Jul 05 2017
(MAGMA) [Arccos(Sqrt(1/3))]; // G. C. Greubel, Nov 18 2017


CROSSREFS

Cf. A195695, A156546, A210974 (in degrees), A243445.
Sequence in context: A089491 A199792 A193960 * A197838 A155534 A154683
Adjacent sequences: A195693 A195694 A195695 * A195697 A195698 A195699


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Sep 23 2011


STATUS

approved



