# Spiral Delone sets and three distance theorem

## TL;DR

This paper characterizes when a constant angle progression on the Fermat spiral forms a Delone set, linking it to the property of the angle being badly approximable.

## Contribution

It establishes a precise condition relating the angle's Diophantine approximation properties to the Delone set formation on the Fermat spiral.

## Key findings

- Constant angle progression forms a Delone set iff the angle is badly approximable.
- Provides a characterization connecting number theory and geometric point sets.
- Enhances understanding of spatial distributions on spirals.

## Abstract

We show that a constant angle progression on the Fermat spiral forms a Delone set if and only if its angle is badly approximable.