On a class of recursive relations for calculating square roots of numbers

We show that a recursive relation for finding square roots of numbers is naturally obtained from an iteration process, and that the relation is solvable in closed form, explaining some results in the literature in an elegant way. We also present a class of recursive relations for finding square roots of numbers which are also solvable in closed form, considerably extending and unifying such recursive relations.

Automated summary

This paper demonstrates that a recursive relation for finding square roots can be naturally derived from an iterative process and can be solved in closed form, providing an elegant explanation for some existing literature. Additionally, a new class of recursive relations for finding square roots, which can also be solved in closed form, is introduced, significantly expanding and unifying the field.