Approximating $\pi$ by numbers in the field $\mathbb{Q}(\sqrt{3})$

Abstract

Using a new integral construction which combines the idea of symmetry suggested by V. Salikhov in 2007 and the integral introduced by Marcovecchio in 2009, we obtain a new bound for approximation to $\pi$ by numbers from the field $\mathbb{Q}\left(\sqrt{3}\right)$.