login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A137914 Decimal expansion of arccos(1/3). 13
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
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
LINKS
Eric Weisstein's World of Mathematics, 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
KEYWORD
cons,nonn
AUTHOR
Rick L. Shepherd, Feb 22 2008
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 06:21 EDT 2024. Contains 370953 sequences. (Running on oeis4.)