Writing pi as sum of arctangents with linear recurrent sequences, Golden   mean and Lucas numbers
  In this paper, we study the representation of pi as sum of arcotangents. In particular, we obtain new identities by using linear recurrent sequences. Moreover, we provide a method in order to express pi as sum of arcotangents involving the Golden mean, the Lucas numbers, and more in general any quadratic irrationality. 
Marco Abrate, Stefano Barbero, Umberto Cerruti, Nadir Murru
math.NT