Writing pi as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers
Marco Abrate, Stefano Barbero, Umberto Cerruti, Nadir Murru
TL;DR
This paper explores novel identities expressing pi as sums of arctangents using linear recurrent sequences, including the Golden mean and Lucas numbers, providing a general method for quadratic irrationals.
Contribution
It introduces a new method to represent pi as sums of arctangents involving quadratic irrationals and linear recurrent sequences, expanding existing identities.
Findings
New identities for pi as sums of arctangents
Method to express pi using Golden mean and Lucas numbers
General approach for quadratic irrationalities
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.
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