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The Scientific World Journal
Volume 2015, Article ID 535469, 3 pages
http://dx.doi.org/10.1155/2015/535469
Research Article

Pick’s Theorem in Two-Dimensional Subspace of

College of Science, Beijing Forestry University, Beijing 100083, China

Received 29 November 2014; Accepted 15 February 2015

Academic Editor: Filippo Cacace

Copyright © 2015 Lin Si. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the Euclidean space , denote the set of all points with integer coordinate by . For any two-dimensional simple lattice polygon , we establish the following analogy version of Pick’s Theorem, , where is the number of lattice points on the boundary of in , is the number of lattice points in the interior of in , and is a constant only related to the two-dimensional subspace including .