Date of Project


Document Type

Honors Thesis

School Name

College of Arts and Sciences



Major Advisor

Dr. Gregory Kelsey

Second Advisor

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.