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 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 (list; constant; graph; refs; listen; history; text; internal format)
 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, 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 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 58. Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author] Jackson, Frank and Weisstein, Eric W., Tetrahedron Eric Weisstein's World of Mathematics, Dihedral Angle Eric Weisstein's World of Mathematics, Trapezo-Rhombic Dodecahedron 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 *) RealDigits[ArcSec[3], 10, 120][[1]] (* Eric W. Weisstein, Jan 09 2019 *) 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

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)