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arXiv · 2310.01091

Lattice angles of lattice polygons

James Dolan·Oleg Karpenkov
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Abstract

This paper is dedicated to a lattice analog to the classical ``sum of interior angles of a polygon theorem''. In 2008, the first formula expressing conditions on the geometric continued fractions for lattice angles of triangles was derived, while the cases of $n$-gons for $n > 3$ remained unresolved. In this paper, we provide the complete solution for all integer $n$. The main results are based on recent advances in geometry of continued fractions.

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James Dolan, Oleg Karpenkov. 2023-10-02. Lattice angles of lattice polygons. https://arxiv.org/abs/2310.01091

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