Writing pi as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers
arXiv:1409.6455 · doi:10.1142/S1793042114500286
Abstract
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.