September 28, 2017 Colloquium

Equal Circle Packing on Flat Klein Bottles - an REU project

Quinn Minnich, Millersville University

Abstract: The study of maximally dense packings of disjoint equal circles is a problem in Discrete Geometry. The optimal densities and arrangements are known for packings of small numbers of equal circles into hard boundary containers, including squares, equilateral triangles and circles. In this presentation, we will explore packings of small numbers of equal circles onto a boundaryless container called a flat Klein bottle. Using numerous figures we will introduce all the basic concepts (including the notion of a flat Klein bottle, an optimal packing and the graph of a packing), illustrate some maximally dense arrangements, and outline the proofs of their optimality. This research was conducted as part of the 2017 REU program at Grand Valley State University.

Location: Wickersham 201, Millersville University

Time: 4:00 - 5:00pm