

A193537


Decimal expansion of cos(Pi/(1+phi)), where phi is the golden ratio.


0



3, 6, 2, 3, 7, 4, 8, 9, 0, 0, 8, 0, 4, 8, 0, 1, 1, 9, 9, 5, 8, 6, 4, 6, 6, 3, 7, 4, 7, 4, 9, 8, 6, 8, 9, 9, 3, 6, 0, 8, 6, 5, 5, 4, 4, 0, 0, 5, 5, 9, 8, 5, 4, 6, 4, 5, 0, 1, 5, 6, 7, 8, 8, 7, 4, 0, 1, 2, 3, 5, 0, 6, 2, 4, 7, 4, 4, 8, 9, 7, 3, 5, 5, 2, 1, 9, 6, 2, 2, 9, 2, 6, 4, 3, 4, 2, 9, 1, 0
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

cos(Pi/(1+phi)) is the first term in the identity:
cos(Pi/(1+phi))+cos(Pi/phi)=0 which when converted to the exponential form gives: e^(i*Pi/(1+phi))+e^(i*Pi/(1+phi))+e^(i*Pi/phi)+e^(i*Pi/phi)=0. In this form it is known as the phi identity because it combines the golden ratio phi with the five fundamental mathematical constants Pi, e, i, 1, 0 that are found in Euler's identity e^(i*Pi) + 1 = 0.


LINKS

Table of n, a(n) for n=0..98.
Frank M. Jackson, Five a day (Letter to Editor), Mathematics Today 506 (2014) 321.


FORMULA

c = cos(Pi/(1+phi)) = cos(2*A180014).


EXAMPLE

0.3623748900804801199586466374749868993608655440055985464501567887401235062...


MATHEMATICA

N[Cos[Pi/(1+GoldenRatio)], 100]


PROG

(PARI) cos((3sqrt(5))*Pi/2) \\ Charles R Greathouse IV, Jul 29 2011


CROSSREFS

Sequence in context: A132120 A021280 A282728 * A319674 A021738 A016614
Adjacent sequences: A193534 A193535 A193536 * A193538 A193539 A193540


KEYWORD

easy,nonn,cons


AUTHOR

Frank M Jackson, Jul 29 2011


STATUS

approved



