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%I #45 Feb 11 2024 23:44:49
%S 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,
%T 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,
%U 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
%N Decimal expansion of arccos(1/3).
%C Dihedral angle in radians of regular tetrahedron.
%C Arccos(1/3) is the central angle of a cube, made by the center and two neighboring vertices. - _Clark Kimberling_, Feb 10 2009
%C Also the complementary tetrahedral angle, Pi-A156546, and therefore related to the magic angle (Pi-2*A195696). - _Stanislav Sykora_, Jan 23 2014
%C Polar angle (or apex angle) of the cone that subtends exactly one third of the full solid angle. - _Stanislav Sykora_, Feb 20 2014
%C Also the acute angle in the rhombi and isosceles trapezoids in the trapezo-rhombic dodecahedron. - _Eric W. Weisstein_, Jan 09 2019
%C Also the angle between the tangent lines to the curves y = sin(x) at y = cos(x) at the points of intersection. - _David Radcliffe_, Jan 17 2023
%H G. C. Greubel, <a href="/A137914/b137914.txt">Table of n, a(n) for n = 1..10000</a>
%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 58.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Tetrahedron.html">Tetrahedron</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DihedralAngle.html">Dihedral Angle</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Trapezo-RhombicDodecahedron.html">Trapezo-Rhombic Dodecahedron</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F arccos(1/3) = arctan(2*sqrt(2)) = 2*arcsin(sqrt(3)/3) = arcsin(2*sqrt(2)/3).
%e 1.2309594173407746821349291782479873757103400093550948390555483336639923144...
%t RealDigits[ArcCos[1/3], 10, 120][[1]] (* _Harvey P. Dale_, Jul 06 2018 *)
%t RealDigits[ArcSec[3], 10, 120][[1]] (* _Eric W. Weisstein_, Jan 09 2019 *)
%o (PARI) acos(1/3)
%o (Magma) SetDefaultRealField(RealField(100)); Arccos(1/3); // _G. C. Greubel_, Aug 20 2018
%Y Cf. A137915 (same in degrees), A019670, A195696, A238238, Platonic solids dihedral angles: A156546 (octahedron), A019669 (cube), A236367 (icosahedron), A137218 (dodecahedron).
%K cons,nonn
%O 1,2
%A _Rick L. Shepherd_, Feb 22 2008
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