

A137914


Decimal expansion of arccos(1/3).


11



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

1,2


COMMENTS

Dihedral angle in radians of regular tetrahedron.
Arccos(1/3) is the central angle of a cube, made by the center and two neighboring vertices.  Clark Kimberling, Feb 10 2009
Also the complementary tetrahedral angle, PiA156546, and therefore related to the magic angle (Pi2*A195696).  Stanislav Sykora, Jan 23 2014
Polar angle (or apex angle) of the cone that subtends exactly one third of the full solid angle.  Stanislav Sykora, Feb 20 2014


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 58.
Jackson, Frank and Weisstein, Eric W., Tetrahedron
Weisstein, Eric W., Dihedral Angle


FORMULA

arccos(1/3) = arctan(2*sqrt(2)) = 2*arcsin(sqrt(3)/3) = arcsin(2*sqrt(2)/3).


EXAMPLE

1.2309594173407746821349291782479873757103400093550948390555483336639923144...


MATHEMATICA

RealDigits[ArcCos[1/3], 10, 120][[1]] (* Harvey P. Dale, Jul 06 2018 *)


PROG

(PARI) acos(1/3)
(MAGMA) SetDefaultRealField(RealField(100)); Arccos(1/3); // G. C. Greubel, Aug 20 2018


CROSSREFS

Cf. A137915 (same in degrees), A019670, A195696, A238238, Platonic solids dihedral angles: A156546 (octahedron), A019669 (cube), A236367 (icosahedron), A137218 (dodecahedron).
Sequence in context: A020823 A021437 A074760 * A098989 A175315 A180186
Adjacent sequences: A137911 A137912 A137913 * A137915 A137916 A137917


KEYWORD

cons,nonn


AUTHOR

Rick L. Shepherd, Feb 22 2008


STATUS

approved



