• Title/Summary/Keyword: Ehrhart 다항식

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Historical review and it's application on the volume of lattice polyhedron - Focused on sequence chapter - (격자다면체 부피에 대한 역사적 고찰 및 그 응용 - 수열 단원에의 응용 -)

  • Kim, Hyang-Sook;Ha, Hyoung-Soo
    • Journal for History of Mathematics
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    • v.23 no.2
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    • pp.101-121
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    • 2010
  • 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.