Spherical friezes

Katie Waddle

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arXiv · 2501.03587

Spherical friezes

Katie Waddle

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Abstract

A fundamental problem in spherical distance geometry aims to recover an $n$-tuple of points on a 2-sphere in $\mathbb{R}^3$, viewed up to oriented isometry, from $O(n)$ input measurements. We solve this problem using algorithms that employ only the four arithmetic operations. Each algorithm recursively produces output data that we arrange into a new type of frieze pattern. These frieze patterns exhibit glide symmetry and a version of the Laurent phenomenon.

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Katie Waddle. 2025-01-07. Spherical friezes. https://arxiv.org/abs/2501.03587

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