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arXiv · 2506.22863

Chabauty Limits of Fermat Spirals

Yohay Ailon Tevet
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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.

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Yohay Ailon Tevet. 2025-09-16. Chabauty Limits of Fermat Spirals. https://doi.org/10.2140/cnt.2025.14.239

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