

A156546


Decimal expansion of the central angle of a regular tetrahedron.


8



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
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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 Pi  arccos(1/3).
The (minimal) central angle of the other four regular polyhedra are as follows:
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., Pi  theta) is the dihedral angle between adjacent faces in regular tetrahedron.  Stanislav Sykora, May 31 2012


LINKS



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.


EXAMPLE

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


MATHEMATICA

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


PROG



CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



