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Abstract
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A Fermat spiral is a set of points of the form
for
. We
prove that the Chabauty limits of Fermat spirals are always closed subgroups of
, and
conclude that no Fermat spirals are dense forests. Furthermore, we show that if
is
badly approximable the Chabauty limits are always lattices, for which we give a
characterisation.
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Keywords
Chabauty topology, Chabauty limit, Fermat spiral, dense
forest, spiral set
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Mathematical Subject Classification
Primary: 11J04, 52C05, 52C99
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Milestones
Received: 30 June 2025
Revised: 26 August 2025
Accepted: 10 September 2025
Published: 24 October 2025
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| © 2025 MSP (Mathematical Sciences
Publishers). |
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