Date of Project
4-29-2023
Document Type
Honors Thesis
School Name
College of Arts and Sciences
Department
Mathematics
Major Advisor
Dr. Gregory Kelsey
Second Advisor
Dr. Michael Ackerman
Abstract
P-adic numbers are numbers valued by their divisibility by high powers of some prime, p. These numbers are an important concept in number theory that are used in major ideas such as the Reimann Hypothesis and Andrew Wiles’ proof of Fermat’s last theorem, and also have applications in cryptography. In this project, we will explore various visualizations of p-adic numbers. In particular, we will look at a mapping of p-adic numbers into the real plane which constructs a fractal similar to a Sierpinski p-gon. We discuss the properties of this map and give formulas for the sharp bounds of its distance distortion, which shows that it is a quasi-isometry.
Recommended Citation
Zopff, Kathleen, "The Sharp Bounds of a Quasi-Isometry of P-adic Numbers in a Subset Real Plane" (2023). Undergraduate Theses. 118.
https://scholarworks.bellarmine.edu/ugrad_theses/118