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 A156546 Decimal expansion of the central angle of a regular tetrahedron. 7
 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 Pi - arccos(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., Pi - theta) 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 Wikipedia, Tetrahedron 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 Pi - arccos(1/3) = 1.910633236249018556..., or, in degrees, 109.471220634490691369245999339962435963006843100... MATHEMATICA RealDigits[Pi-ArcCos[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, A247412. 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

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Last modified December 15 01:20 EST 2018. Contains 318141 sequences. (Running on oeis4.)