# 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.