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arXiv · 1707.04808

Recurrent Theme of Pick's Theorem

Jacek M. Kowalski
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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.

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Jacek M. Kowalski. 2017-07-16. Recurrent Theme of Pick's Theorem. https://arxiv.org/abs/1707.04808

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