Graduation Year
2024
Document Type
Campus Only Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
Reader 1
Winston Ou
Reader 2
Asuman Aksoy
Terms of Use & License Information
Rights Information
2024 Ella R Young
Abstract
Following the outline of the 2010 book The Erdős Distance Problem by Julia Garibaldi, Alex Iosevich, and Steven Senger, this thesis presents in greater detail the development of results in the Erdős distance problem in discrete geometry.
This problem asks the question: given n points in the plane, what is the minimum number of distinct distances determined by these points? We provide detailed proofs for results illuminated by Erdős, Moser, Székely, Solymosi, and Tóth.
Additionally, the thesis provides necessary definitions and results in the fields of graph theory and incidence theory, including prominent results by Szemerédi, Trotter, and Beck.
The thesis aims to provide a detailed and accurate companion to the literature surrounding this topic, with all theorems, lemmas, and corollaries rigorously proven.
Recommended Citation
Young, Ella, "An Exploration of Results in the Advancement of the Erdős Distance Problem" (2024). Scripps Senior Theses. 2273.
https://scholarship.claremont.edu/scripps_theses/2273
This thesis is restricted to the Claremont Colleges current faculty, students, and staff.
