

A195693


Decimal expansion of arctan(1/r), where r = (1+sqrt(5))/2 (the golden ratio).


5



5, 5, 3, 5, 7, 4, 3, 5, 8, 8, 9, 7, 0, 4, 5, 2, 5, 1, 5, 0, 8, 5, 3, 2, 7, 3, 0, 0, 8, 9, 2, 6, 8, 5, 2, 0, 0, 3, 5, 0, 2, 3, 8, 2, 2, 7, 0, 0, 7, 1, 6, 3, 2, 3, 3, 3, 8, 2, 6, 9, 6, 0, 3, 7, 1, 6, 8, 5, 5, 1, 6, 9, 4, 8, 8, 6, 8, 1, 3, 9, 7, 0, 0, 6, 7, 0, 8, 5, 6, 4, 3, 4, 3, 0, 8, 5, 3, 2, 0, 7
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OFFSET

0,1


COMMENTS

Radian measure of half the smaller angle in the golden rhombus.  Eric W. Weisstein, Dec 11 2018


LINKS

Table of n, a(n) for n=0..99.
HeiChi Chan, Machintype formulas expressing Pi in terms of phi, Fibonacci Quart. 46/47 (2008/2009), no. 1, 3237.
Eric Weisstein's World of Mathematics, Golden Rhombus


EXAMPLE

arctan(1/r) = 0.5535743588970452515085327300892685200... .
tan(0.5535743588970452515085327300...) = 1/(golden ratio).
cot(0.5535743588970452515085327300...) = (golden ratio).


MATHEMATICA

(See also A195692.)
RealDigits[ArcCot[GoldenRatio], 10, 100][[1]] (* or *) RealDigits[(Pi  ArcTan[4/3])/4, 10, 100][[1]] (* Eric W. Weisstein, Dec 11 2018 *)


CROSSREFS

Cf. A001622, A175288, A195692, A195694.
Sequence in context: A291040 A089486 A199617 * A232813 A267033 A306982
Adjacent sequences: A195690 A195691 A195692 * A195694 A195695 A195696


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Sep 22 2011


STATUS

approved



