This paper is a summary of some interesting properties of the Cantor ternary set and a few investigations of other general Cantor sets. The ternary set is discussed in detail, followed by an explanation of three ways of creating general Cantor sets developed by the author. The focus is on the dimension of these sets, with a detailed explanation of Hausdorff dimension included, and how they act as interesting examples of fractal sets.
I am a native of St. Louis, Missouri, graduating from St. Louis University High in 2005 and then attending Rockhurst University in Kansas City, Missouri as an undergraduate. I completed this research paper as a result of my role in a larger project using fractals to explore the relationship between art and math. This project, funded by the James and Elizabeth Monahan Summer Research Fellowship at Rockhurst, was undertaken during Summer 2008, with further research extended as a final project in the Mathematics Seminar course at Rockhurst in Spring 2009. I graduated from Rockhurst University in May 2009 with three bachelors' degrees: a Bachelor of Science in Mathematics, a Bachelor of Arts in Theology, and a Bachelor of Science in Business Administration. For one year after my graduation I am a volunteer in the Alum Service Corps, a program for graduates of Jesuit high schools, serving as a math teacher at Regis Jesuit High School in Denver, Colorado, after which I plan on attending graduate school in mathematics. /p>
"An Exploration of the Cantor Set,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 11:
1, Article 1.
Since January 15, 2017