A two dimensional analog of the three gap theorem

Yury Kochetkov; Alexandr Osipov

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arXiv · 2308.01848

A two dimensional analog of the three gap theorem

Yury Kochetkov·Alexandr Osipov

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Abstract

For a two dimensional vector $\bar v=(α,β)$, where $α>0, β>0$ are irrational numbers independent over $\mathbb{Q}$, we consider the set $D_n=\{(iα\,{\rm mod}\,1,iβ\,{\rm mod}\,1),i=1,\ldots,n\}$ in a two dimensional torus and the partition of this torus into Voronoi cells. Areas and forms of these cells are the subject of this experimental work.

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Yury Kochetkov, Alexandr Osipov. 2023-08-03. A two dimensional analog of the three gap theorem. https://arxiv.org/abs/2308.01848

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