Superoptimal continued fractions
Number Theory
2025-12-09 v2 Dynamical Systems
Abstract
Motivated by the optimal continued fractions studied independently by Selenius and Bosma, we define and introduce algorithms producing superoptimal continued fraction expansions of irrationals. The convergents of these expansions simultaneously provide arbitrarily good rational approximations and converge arbitrarily quickly.
Keywords
Cite
@article{arxiv.2508.19743,
title = {Superoptimal continued fractions},
author = {Slade Sanderson},
journal= {arXiv preprint arXiv:2508.19743},
year = {2025}
}
Comments
15 pages, 5 figures. Includes new figure (Fig. 4) and other small improvements following referee suggestions. Accepted by Proc. Amer. Math. Soc