Lattice angles of lattice polygons

2023/10/02 by James Dolan, Dolan, James, Oleg Karpenkov +1
Mathematics · #11A55 #11H06 #52C05 #Combinatorics (math.CO) #FOS: Mathematics #History and Theory of Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2310.01091

openalex publication_date 2023/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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