A Spigot-Algorithm for Square-Roots: Explained and Extended
Discrete Mathematics
2023-12-27 v1
Abstract
This work presents and extends a known spigot-algorithm for computing square-roots, digit-by-digit, that is suitable for calculation by hand or an abacus, using only addition and subtraction. We offer an elementary proof of correctness for the original algorithm, then present a corresponding spigot-algorithm for computing cube-roots. Finally, we generalize the algorithm, so as to find -th roots, and show how to optimize the algorithm for any . The resulting algorithms require only integer addition and subtraction.
Cite
@article{arxiv.2312.15338,
title = {A Spigot-Algorithm for Square-Roots: Explained and Extended},
author = {Mayer Goldberg},
journal= {arXiv preprint arXiv:2312.15338},
year = {2023}
}