%N Decimal expansion of cos(Pi/(1+phi)), where phi is the golden ratio.
%C cos(Pi/(1+phi)) is the first term in the identity:
%C 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.
%H Frank M. Jackson, <a href="http://www.researchgate.net/publication/292983417">Five a day (Letter to Editor)</a>, Mathematics Today 50-6 (2014) 321.
%F c = cos(Pi/(1+phi)) = cos(2*A180014).
%o (PARI) cos((3-sqrt(5))*Pi/2) \\ _Charles R Greathouse IV_, Jul 29 2011
%A _Frank M Jackson_, Jul 29 2011