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A019863
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Decimal expansion of sine of 54 degrees.
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11
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8, 0, 9, 0, 1, 6, 9, 9, 4, 3, 7, 4, 9, 4, 7, 4, 2, 4, 1, 0, 2, 2, 9, 3, 4, 1, 7, 1, 8, 2, 8, 1, 9, 0, 5, 8, 8, 6, 0, 1, 5, 4, 5, 8, 9, 9, 0, 2, 8, 8, 1, 4, 3, 1, 0, 6, 7, 7, 2, 4, 3, 1, 1, 3, 5, 2, 6, 3, 0, 2, 3, 1, 4, 0, 9, 4, 5, 1, 2, 2, 4, 8, 5, 3, 6, 0, 3, 6, 0, 2, 0, 9, 4, 6, 9, 5, 5, 6, 8
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OFFSET
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0,1
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COMMENTS
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Midsphere radius of regular icosahedron with unit edges.
Also half of the golden ratio (A001622). - Stanislav Sykora, Jan 30 2014
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LINKS
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Stanislav Sykora, Table of n, a(n) for n = 0..2000
Wikipedia, Exact trigonometric constants
Wikipedia, Platonic solid
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FORMULA
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Equals [1+sqrt(5)]/4 = cos(Pi/5) = sin(3Pi/10). - R. J. Mathar, Jun 18 2006
Equals 2F1(4/5,1/5;1/2;3/4) / 2 = A019827 + 1/2. - R. J. Mathar, Oct 27 2008
Equals A001622 / 2. - Stanislav Sykora, Jan 30 2014
phi / 2 = (i^(2/5) + i^(-2/5)) / 2 = i^(2/5) - (sin(Pi/5))*i = i^(-2/5) + (sin(Pi/5))*i = i^(2/5) - (cos(3*Pi/10))*i = i^(-2/5) + (cos(3*Pi/10))*i. - Jaroslav Krizek, Feb 03 2014
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EXAMPLE
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0.80901699437494742410229341718281905886015458990288143106772431135263...
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MAPLE
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Digits:=100; evalf((1+sqrt(5))/4); # Wesley Ivan Hurt, Mar 27 2014
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MATHEMATICA
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RealDigits[(1 + Sqrt[5])/4, 10, 111] (* Robert G. Wilson v *)
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PROG
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(PARI) (1+sqrt(5))/4 \\ Charles R Greathouse IV, Jan 16 2012
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CROSSREFS
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Cf. A019827, A001622.
Cf. Platonic solids midradii:
A020765 (tetrahedron),
A020761 (octahedron),
A010503 (cube),
A239798 (dodecahedron). [Stanislav Sykora, Mar 27 2014]
Sequence in context: A076350 A197617 A005076 * A198820 A138285 A085291
Adjacent sequences: A019860 A019861 A019862 * A019864 A019865 A019866
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KEYWORD
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nonn,cons,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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