Date of Project
College of Arts and Sciences
Dr. Gregory Kelsey
Dr. Michael Ackerman
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.
Zopff, Kathleen, "The Sharp Bounds of a Quasi-Isometry of P-adic Numbers in a Subset Real Plane" (2023). Undergraduate Theses. 118.