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Full-Text Articles in Physical Sciences and Mathematics
Geometries Gon Wild, Naat Ambrosino
Geometries Gon Wild, Naat Ambrosino
Undergraduate Theses
A circle is mathematically defined as the collection of points a given distance away from a set point. Thus, the appearance of a circle varies dramatically across different metrics—for example, the taxicab metric (as popularized by Krause and Reynolds) has a circle that is a Euclidean square. As such, metrics can be partially defined by the appearance of their unit circles. This paper focuses on creating and analyzing an infinite set of metrics defined by their circles being regular polygons. Additionally, it provides a method of exactly generating a regular n-gon given a center, included point, and specified orientation.
The Sharp Bounds Of A Quasi-Isometry Of P-Adic Numbers In A Subset Real Plane, Kathleen Zopff
The Sharp Bounds Of A Quasi-Isometry Of P-Adic Numbers In A Subset Real Plane, Kathleen Zopff
Undergraduate Theses
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 …