Pick's Theorem in two-dimensional lattices

In this article, a generalization of Pick's Theorem is presented, which establishes an expression for the area of simple polygons whose vertices are points of an arbitrary two-dimensional lattice, in terms of the determinant and the number of lattice points inside the polygon and on its boundar...

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Bibliographic Details
Authors: Strey, Eleonesio, Machado, Suzana Carletti, Strey, Giselle Ribeiro de Azeredo Silva
Format: article
Status:Published version
Publication Date:2025
Country:Brasil
Institution:Universidade Federal de Santa Maria (UFSM)
Repository:Revista Ciência e Natura (Online)
Language:Portuguese
OAI Identifier:oai:ojs.pkp.sfu.ca:article/87983
Online Access:https://periodicos.ufsm.br/cienciaenatura/article/view/87983
Access Level:Open access
Keyword:Pick's Theorem
Polygon areas
Lattices
Teorema de Pick
Áreas de polígonos
Reticulados
Description
Summary:In this article, a generalization of Pick's Theorem is presented, which establishes an expression for the area of simple polygons whose vertices are points of an arbitrary two-dimensional lattice, in terms of the determinant and the number of lattice points inside the polygon and on its boundary.