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A137218
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Decimal expansion of the argument of -1 + 2*i.
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10
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2, 0, 3, 4, 4, 4, 3, 9, 3, 5, 7, 9, 5, 7, 0, 2, 7, 3, 5, 4, 4, 5, 5, 7, 7, 9, 2, 3, 1, 0, 0, 9, 6, 5, 8, 4, 4, 1, 2, 7, 1, 2, 1, 7, 5, 3, 9, 7, 3, 6, 7, 3, 1, 7, 4, 2, 9, 8, 4, 0, 5, 3, 8, 4, 8, 7, 4, 1, 0, 6, 0, 6, 7, 3, 0, 8, 8, 4, 6, 2, 0, 4, 6, 1, 4, 6, 1, 7, 6, 9, 6, 6, 5, 5, 9, 4, 6, 4, 2, 6, 5, 4, 7, 6, 0
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OFFSET
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1,1
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COMMENTS
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Gives closed forms for many arctangent values:
arctan(2) = Pi - a, arctan(1/2) = a - Pi/2,
arctan(3) = a - Pi/4, arctan(1/3) = 3*Pi/4 - a,
arctan(7) = 7*Pi/4 - 2*a, arctan(1/7) = 2*a - 5*Pi/4,
arctan(4/3) = 2*a - Pi and arctan(3/4) = 3*Pi/2 - 2*a.
Dihedral angle in the dodecahedron (radians). - R. J. Mathar, Mar 24 2012
Larger interior angle (in radians) of a golden rhombus; A105199 is the smaller interior angle. - Eric W. Weisstein, Dec 17 2018
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LINKS
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FORMULA
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EXAMPLE
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2.0344439357957027354455779231...
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MATHEMATICA
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RealDigits[Pi - ArcTan[2], 10, 120][[1]] (* Harvey P. Dale, Aug 08 2014 *)
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PROG
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(PARI)
default(realprecision, 120);
acos(-1/sqrt(5)) \\ or
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CROSSREFS
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Cf. A105199 (smaller interior angle of the golden rhombus).
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KEYWORD
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AUTHOR
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Matt Rieckman (mjr162006(AT)yahoo.com), Mar 06 2008
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EXTENSIONS
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Corrected a typo in the sequence Matt Rieckman (mjr162006(AT)yahoo.com), Feb 05 2010
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STATUS
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approved
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