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A195723 Decimal expansion of arctan(golden ratio). 6
1, 0, 1, 7, 2, 2, 1, 9, 6, 7, 8, 9, 7, 8, 5, 1, 3, 6, 7, 7, 2, 2, 7, 8, 8, 9, 6, 1, 5, 5, 0, 4, 8, 2, 9, 2, 2, 0, 6, 3, 5, 6, 0, 8, 7, 6, 9, 8, 6, 8, 3, 6, 5, 8, 7, 1, 4, 9, 2, 0, 2, 6, 9, 2, 4, 3, 7, 0, 5, 3, 0, 3, 3, 6, 5, 4, 4, 2, 3, 1, 0, 2, 3, 0, 7, 3, 0, 8, 8, 4, 8, 3, 2, 7, 9, 7, 3, 2, 1, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
The polar angle, in radians, of the cone circumscribed to a regular icosahedron from one of its vertices. - Stanislav Sykora, Feb 15 2014
The angle between the diagonal and the shorter side of a golden rectangle. - Amiram Eldar, May 18 2021
LINKS
FORMULA
Equals arccos(sqrt((5-sqrt(5))/10)). - Stanislav Sykora, Feb 15 2014
Equals Pi/2 - A195693. - Amiram Eldar, May 18 2021
EXAMPLE
arctan((1+sqrt(5))/2) = 1.0172219678978513677227...
MATHEMATICA
r=GoldenRatio; N[ArcTan[r], 100]
RealDigits[%] (* A195723 *)
PROG
(PARI) atan((1+sqrt(5))/2) \\ G. C. Greubel, Aug 20 2018
(Magma) SetDefaultRealField(RealField(100)); Arctan((1+Sqrt(5))/2); // G. C. Greubel, Aug 20 2018
CROSSREFS
Sequence in context: A176704 A289917 A198415 * A138996 A010141 A316247
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Sep 23 2011
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)