Date of Submission

Spring 2016

Academic Programs and Concentrations

Mathematics

Project Advisor 1

Ethan Bloch

Abstract/Artist's Statement

A lattice stick knot is a closed curve in R3 composed of finitely many line segments, sticks, that lie parallel to the three coordinate axes in R3, such that the line segments meet at points in the 3-dimensional integer lattice. The lattice stick number of a knot is the minimal number of sticks required to realize that knot as a lattice stick knot. A right angle lattice projection is a projection of a knot in R3onto the plane such that the edges of the projection lie parallel to the two coordinate axes in the plane, and the edges meet at points in the 2-dimensional integer lattice. This project examines when right angle lattice projections are projections of lattice stick knots, with the aim to get an upper bound on lattice stick number.

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