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A195696 Decimal expansion of arccos(sqrt(1/3)) and of arcsin(sqrt(2/3)) and arctan(sqrt(2)). 10
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 (list; constant; graph; refs; listen; history; text; internal format)
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 second-order 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 dipole-dipole 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.

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

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

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Last modified August 20 15:02 EDT 2017. Contains 290835 sequences.