

A156546


Decimal expansion of the central angle of a regular tetrahedron.


5



1, 9, 1, 0, 6, 3, 3, 2, 3, 6, 2, 4, 9, 0, 1, 8, 5, 5, 6, 3, 2, 7, 7, 1, 4, 2, 0, 5, 0, 3, 1, 5, 1, 5, 5, 0, 8, 4, 8, 6, 8, 2, 9, 3, 9, 0, 0, 2, 0, 0, 1, 0, 9, 8, 1, 9, 1, 9, 3, 9, 6, 2, 5, 8, 6, 4, 3, 8, 2, 4, 0, 9, 1, 8, 0, 7, 9, 5, 2, 9, 1, 0, 7, 7, 4, 7, 8, 3, 2, 0, 5, 1, 7, 1, 2, 5, 6, 1, 4, 6, 8, 4, 3, 2, 0
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

If O is the center of a regular tetrahedron ABCD, then the central angle AOB is this number; exact value is piarccos(1/3).
The (minimal) central angle of the other four regular polyhedra are as follows:
 cube: A137914,
 octahedron: A019669,
 dodecahedron: A156547,
 icosahedron: A105199.
Dihedral angle of two adjacent faces of the octahedron.  R. J. Mathar, Mar 24 2012
Best known as "tetrahedral angle" theta (e.g., in chemistry). Its Pi complement (i.e., Pitheta) is the dihedral angle between adjacent faces in regular tetrahedron.  Stanislav Sykora, May 31 2012
Also twice the magic angle (A195696).  Stanislav Sykora, Nov 14 2013


LINKS

Table of n, a(n) for n=1..105.
Wikipedia, Octahedron
Wikipedia, Tetrahedral molecular geometry


FORMULA

Start with vertices (1,1,1), (1,1,1,), (1,1,1), and (1,1,1) and apply the formula for cosine of the angle between two vectors.
Two times A195696.  R. J. Mathar, Mar 24 2012


EXAMPLE

Piarccos(1/3)=1.910633236249018556..., or, in degrees,
109.471220634490691369245999339962435963006843100...


MATHEMATICA

RealDigits[PiArcCos[1/3], 10, 120][[1]] (* Harvey P. Dale, Aug 25 2011 *)


PROG

(PARI) acos(1/3) \\ Charles R Greathouse IV, Aug 30 2013


CROSSREFS

Cf. A195696.
Cf. Platonic solids dihedral angles: A137914 (tetrahedron), A019669 (cube), A236367 (icosahedron), A137218 (dodecahedron).  Stanislav Sykora, Jan 23 2014
Sequence in context: A227817 A102209 A222131 * A154839 A064733 A020841
Adjacent sequences: A156543 A156544 A156545 * A156547 A156548 A156549


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Feb 09 2009


STATUS

approved



