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A156546
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Decimal expansion of the central angle of a regular tetrahedron.
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1
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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; internal format)
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OFFSET
| 1,2
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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.
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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.
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EXAMPLE
| pi-arccos(1/3)=1.910633236249018556..., or, in degrees,
109.471220634490691369245999339962435963006843100...
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MATHEMATICA
| RealDigits[Pi-ArcCos[1/3], 10, 120][[1]] (* From Harvey P. Dale, Aug 25 2011 *)
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CROSSREFS
| Sequence in context: A070060 A176980 A102209 * A154839 A064733 A020841
Adjacent sequences: A156543 A156544 A156545 * A156547 A156548 A156549
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KEYWORD
| nonn,cons
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Feb 09 2009
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