Generating a Finite Subset of a Lattice of Convex Sets
Department
Electrical and Computer Engineering
Major
Electrical Engineering
Research Advisor
Insall, Matt
Advisor's Department
Mathematics and Statistics
Funding Source
UMR Opportunities for Undergraduate Research Experiences (OURE)
Abstract
Geometric arrangements of (finitely many) generators in the lattice of convex subsets in the plane can have a profound effect on the lattice generated. We examine the example of a triangle with three finite line segments. This leads to the following conjecture:
[Formulas inserted] Conditions for the generation of a finite sublattice will be discussed for an equilateral triangle and all other regular n-gons replacing the triangle.
Biography
Michael Nolte is a sophomore in Electrical Engineering at the University of Missouri--Rolla. His interest in this topic began upon reading Insall’s paper Geometric Conditions for Local Finiteness of a Lattice of Convex Sets. Dr. Insall and Michael have worked together on this project since last fall. In that time, Michael has had the opportunity to talk on this research at the Joint Mathematics Meetings in San Antonio, Texas and at the Graduate Student Seminar on campus. Michael also participates in the mathematics honor society, Kappa Mu Epsilon, as the recruitment chair.
Research Category
Natural Sciences
Presentation Type
Poster Presentation
Document Type
Poster
Presentation Date
12 Apr 2006, 1:00 pm
Generating a Finite Subset of a Lattice of Convex Sets
Geometric arrangements of (finitely many) generators in the lattice of convex subsets in the plane can have a profound effect on the lattice generated. We examine the example of a triangle with three finite line segments. This leads to the following conjecture:
[Formulas inserted] Conditions for the generation of a finite sublattice will be discussed for an equilateral triangle and all other regular n-gons replacing the triangle.
