## Classification of rational angles in plane lattices

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Roberto Dvornicich, Francesco Veneziano and Umberto Zannier
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**59**(2022), 191-226 Request permission

## Abstract:

This paper is concerned with configurations of points in a plane lattice which determine angles that are rational multiples of $\pi$. We shall study how many such angles may appear in a given lattice and in which positions, allowing the lattice to vary arbitrarily.

This classification turns out to be much less simple than could be expected, leading even to parametrizations involving rational points on certain algebraic curves of positive genus.

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## Additional Information

**Roberto Dvornicich**- Affiliation: Department of mathematics, University of Pisa, Largo Bruno PontecorvoÂ 5, 56127 Pisa, Italy
- MR Author ID: 61055
- Email: roberto.dvornicich@unipi.it
**Francesco Veneziano**- Affiliation: Department of mathematics, University of Genova, Via DodecanesoÂ 35, 16146 Genova, Italy
- MR Author ID: 966417
- ORCID: 0000-0002-2225-7769
- Email: veneziano@dima.unige.it
**Umberto Zannier**- Affiliation: Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
- MR Author ID: 186540
- Email: umberto.zannier@sns.it
- Received by editor(s): June 8, 2020
- Published electronically: August 31, 2021
- © Copyright 2021 American Mathematical Society
- Journal: Bull. Amer. Math. Soc.
**59**(2022), 191-226 - MSC (2020): Primary 11H06, 14G05, 11D61, 51M05
- DOI: https://doi.org/10.1090/bull/1723
- MathSciNet review: 4390499