Year: 2025
Type: article
Abstract: A Fermat spiral is a set of points of the form $\sqrt{n}e^{2πiαn}$ for $α\in \mathbb{R}$. In this paper we prove that the Chabauty limits of Fermat spirals are always closed subgroups of $\mathbb{R}^2$, and conclude that no Fermat spirals are dense forests. Furthermore, we show that if $α$ is badly approximable the Chabauty limits are always lattices, for which we give a characterisation.
Source: Combinatorics and Number Theory
Author: Yohay Ailon Tevet
Institution: Tel Aviv University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415529271