Year: 2025
Type: article
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.
DOI: 10.5802/jtnb.1345
Authors: James Dolan, Oleg Karpenkov
Institution: University of Liverpool
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4416741070