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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
Also the acute angle in the rhombi and isosceles trapezoids in the trapezo-rhombic dodecahedron. - Eric W. Weisstein, Jan 09 2019
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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
Eric Weisstein's World of Mathematics, Dihedral Angle
Eric Weisstein's World of Mathematics, Trapezo-Rhombic Dodecahedron
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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 *)
RealDigits[ArcSec[3], 10, 120][[1]] (* Eric W. Weisstein, Jan 09 2019 *)
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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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