Recurrent Theme of Pick's Theorem
History and Overview
2017-07-18 v1
Abstract
We review and possibly add some new variant to the existing derivations of the formula for the area of Jordan lattice polygons drawn on two-dimensional lattices. The formula is known as Pick's theorem and is related to the number theory elementary result-Bezout lemma. It is pointed out that Euclidean algorithm can be easily used in construction of infinite number of distinct primitive cells for any two-dimensional lattice. Pick's formula itself can also be obtained in an elementary "cut and re-assemble" finite process.
Cite
@article{arxiv.1707.04808,
title = {Recurrent Theme of Pick's Theorem},
author = {Jacek M. Kowalski},
journal= {arXiv preprint arXiv:1707.04808},
year = {2017}
}
Comments
13 pages, 3 figures