January 24, 2012 -
5:40 pm to 6:30 pm
Location: Cupples I, Room 199 |
Hosts: Prof. Quo-Shin Chi, Karli McBryde & Rachel Blake
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 three equal circles into a boundaryless container called a flat torus. Using numerous figures we will introduce all the basic concepts (including the notion of a flat torus, an optimal packing and the graph of a packing), demonstrate many maximally dense arrangements, and outline the proofs of their optimality. This research was conducted as part of the 2011 REU program at Grand Valley State University.
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