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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 therecurrence relations for the constant $1$. Computational test shows thatapplication of this set of the Vi\`ete-like recurrence relations results in arapid convergence to unity.

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