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A137914
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Decimal expansion of arccos(1/3).
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11
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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
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1,2
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COMMENTS
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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, Pi-A156546, and therefore related to the magic angle (Pi-2*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
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LINKS
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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
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FORMULA
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arccos(1/3) = arctan(2*sqrt(2)) = 2*arcsin(sqrt(3)/3) = arcsin(2*sqrt(2)/3).
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EXAMPLE
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1.2309594173407746821349291782479873757103400093550948390555483336639923144...
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MATHEMATICA
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RealDigits[ArcCos[1/3], 10, 120][[1]] (* Harvey P. Dale, Jul 06 2018 *)
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PROG
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(PARI) acos(1/3)
(MAGMA) SetDefaultRealField(RealField(100)); Arccos(1/3); // G. C. Greubel, Aug 20 2018
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CROSSREFS
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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
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KEYWORD
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cons,nonn
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AUTHOR
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Rick L. Shepherd, Feb 22 2008
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STATUS
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approved
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