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

## TL;DR

This paper introduces a set of Viète-like recurrence relations for the constant 1, derived from nested radicals related to pi, demonstrating rapid convergence to unity through computational tests.

## Contribution

It presents a novel set of recurrence relations for the constant 1 based on a Viète-like formula involving nested radicals, expanding the mathematical understanding of such relations.

## Key findings

- Recurrence relations converge rapidly to 1
- Derived from nested radicals related to pi
- Validated through computational tests

## 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.