Honors Program Theses
Award/Availability
Open Access Honors Program Thesis
Keywords
Hyperbolic spaces; Geodesics (Mathematics);
Abstract
Hyperbolic geometry is a beautiful, non-Euclidean space that hosts spectacular patterns and infinite designs. To learn about this space, this paper will focus on how linear fractional transformations act on this space and the patterns that reveal themselves. To expand on this, I will construct a fundamental domain under these mappings and explore the coding of closed geodesics on the fundamental domain, which requires an understanding of continued fractions. My research will then be applied to two copies of the hyperbolic plane. My goal is to understand fundamental regions in this space and eventually the geodesics.
This paper is intended for a second- or third-year mathematics student who has completed multivariable calculus and a semester of modern algebra. Some proofs or examples may require some understanding of real analysis.
Year of Submission
2008
Department
Department of Mathematics
University Honors Designation
A thesis submitted in partial fulfillment of the requirements for the designation University Honors
Date Original
5-2008
Object Description
1 PDF file (21 pages)
Copyright
©2008 Alyssa Jesse Soenksen
Language
en
File Format
application/pdf
Recommended Citation
Soenksen, Alyssa Jesse, "A Fundamental Region on Two Copies of the Hyperbolic Plane" (2008). Honors Program Theses. 758.
https://scholarworks.uni.edu/hpt/758
Comments
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