Pick's Theorem in Two-Dimensional Subspace of R3. (23rd February 2015)

• Record Type: Journal Article
• Authors: Si, Lin
• Other Names: Cacace Filippo Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2015(2015)
• Publication Date: 2015-02-23
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2015/535469
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : In the Euclidean space R 3, denote the set of all points with integer coordinate by Z 3 . For any two-dimensional simple lattice polygon P, we establish the following analogy version of Pick's Theorem, k I P + 1 / 2 B P - 1, where B P is the number of lattice points on the boundary of P in Z 3, I P is the number of lattice points in the interior of P in Z 3, and k is a constant only related to the two-dimensional subspace including P .