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Historical review and it's application on the volume of lattice polyhedron - Focused on sequence chapter -  

Kim, Hyang-Sook (Department of Computer Science, School of Computer Aided Science and Institute of Basic Science, Inje University)
Ha, Hyoung-Soo (Seong Seo High School)
Publication Information
Journal for History of Mathematics / v.23, no.2, 2010 , pp. 101-121 More about this Journal
Abstract
This article includes an introduction, a history of Pick's theorem on lattice polyhedron and its proof, Reeve's theorem on 3-dimensional lattice polyhedrons extended from the Pick's theorem and Ehrhart polynomial generalized as an n-dimensional lattice polyhedron, and then shows the relationship between the volume of 3-dimensional polyhedron and the number of its lattice points by means of Reeve's theorem. It is aimed to apply the relationship to the visualization of sums in sequences.
Keywords
lattice plane; Pick's theorem; lattice space; Reeve's theorem; Ehrhart polynomial; lattice polyhedron;
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