Degree Type

Thesis

Degree Name

Bachelor of Science (BS)

Date Information

December 2016

Department

Mathematics

First Advisor

Pedro Poitevin

Abstract

The purpose of this research project is to analyze the scholarly article The Plane Symmetry Groups: Their Recognition and Notation by Doris Schattschneider. In this article, Schattschneider discusses an application of abstract algebra which is useful in art as well as crystallography: frieze groups and wallpaper groups. I was interested in pursuing this topic because it combines mathematics with its applications, particularly with my own interest in chemistry. The article provides a compiled resource of terminology and rules of these groups, but not one which was easily accessible to undergraduate students. In my research, I elaborated on the descriptions of certain types of periodic patterns to add to the accessibility, and analyzed a few designs to prove their classification based on the rules from Schattschneider's article. I found that this resource provided a good source of rules for which mathematical proofs could be based, and proved the classification of two different periodic plane designs.

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