Undergraduate Honors Thesis

Abstract

• A Descartes quadruple is a set of four mutually tangent circles. A Descartes quadruples generates what is known as an Apollonian circle packing. By studying the ratios of the circles' curvatures, two distinct types of symmetric packings quadruples appear. We give parameterizations of these Descartes quadruples and count how many packings of each type are contained by a given enclosing circle.

Creator

• Kertzer, Clyde

Date Awarded

• 2024-04-10

Academic Affiliation

• Mathematics

Advisor

• Stange, Katherine

Granting Institution

• University of Colorado Boulder

Subject

• Number Theory
• Apollonian Circle Packings
• Descartes Quadriples

Last Modified

• 2024-04-22

Resource Type

• Undergraduate Honors Thesis

Rights Statement

• In Copyright

Language

• English [eng]

Relationships

In Collection:

• Arts and Sciences Honors Program

Items

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