A set of the Vi\`ete-like recurrence relations for the unity constant

Abstract

Using a simple Vi\`ete-like formula for $\pi$ based on the nested radicals $a_k = \sqrt{2 + a_{k-1}}$ and $a_1 = \sqrt{2}$, we derive a set of the recurrence relations for the constant $1$. Computational test shows that application of this set of the Vi\`ete-like recurrence relations results in a rapid convergence to unity.