Circle Packing in Euclidean and Hyperbolic Geometries

Given a graph that defines a triangulation of a simply connected surface, it is possible to associate a radius with each vertex so that the vertices represent centers of circles, and the edges denote patterns of tangency. Such a configuration of circles is called a circle packing. We shall give evidence for the existence and uniqueness of circle packings generated by such graphs, as well as an explanation of the algorithms used to find and output a circle packing on the complex plane and hyperbolic disc.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2008

Author dc:creator

• Wilkerson, Mary Elizabeth

Chair dc:contributor.committeechair

• Floyd, William J.

Committee members dc:contributor.committeemember

• Haskell, Peter E.
• Thomson, James E.

• Circle Packings
• Uniform Neighbor Model

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-05082008-175931

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/32390