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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.

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,changed

AUTHOR

Rick L. Shepherd, Feb 22 2008

STATUS

approved

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Last modified January 21 15:20 EST 2019. Contains 319350 sequences. (Running on oeis4.)