Pick's Theorem in Two-Dimensional Subspace of R^3

TL;DR

This paper extends Pick's theorem to simple lattice polygons situated within two-dimensional subspaces of three-dimensional space, providing a new perspective on lattice geometry in higher dimensions.

Contribution

It introduces a version of Pick's theorem applicable to polygons in 2D subspaces of R^3, expanding the theorem's applicability beyond the plane.

Findings

Established a Pick's theorem variant for 2D lattice polygons in R^3

Provided a mathematical framework for lattice polygons in higher-dimensional spaces

Enhanced understanding of lattice point enumeration in subspaces

Abstract

In this note, we given a version of Pick's theorem for the simple lattice polygon in two-dimensional subspace of R^3.