Abstract

A Fermat spiral is a set of points of the form $\sqrt{n}{e}^{2\pi i\alpha n}$ for $\alpha \in ℝ$. We prove that the Chabauty limits of Fermat spirals are always closed subgroups of ${ℝ}^2$, and conclude that no Fermat spirals are dense forests. Furthermore, we show that if $\alpha$ is badly approximable the Chabauty limits are always lattices, for which we give a characterisation.

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