## Senior Independent Study Theses

#### Abstract

The focus of my independent study thesis is the connection between math and knitting, specifically in relation to representing symmetry and frieze patterns. The beginning chapter of the thesis will give an introduction to group theory starting with general background on groups and building into their relationship with symmetry. The chapter will open by describing the various properties of groups. Next, there will be a discussion of the various types of groups including cyclic groups, permutation groups, and abelian groups. In defining each group, the various properties and their significance will be given along with examples to build understanding. After discussing the various types of groups, the discussion will move on to describe isomorphisms and what makes two groups isomorphic. Once an understanding of the basics of group theory has been given, the next chapter will narrow the focus onto symmetry groups and frieze patterns. The chapter will begin with the definition of an isometry and a description of the different types of rigid motion. After showing that an isometry is a linear transformation, the chapter will state the definition of a symmetry group, along with the properties of a symmetry group and their significance. Next, there will be a discussion of wallpaper groups and their relationship with symmetry groups. Narrowing the focus onto frieze patterns, the seven different symmetrical classifications of frieze patterns will be described with examples of how they can be drawn and how they can be written as a set of isometries. The final part of the thesis will look at the relationship between frieze patterns and knitting and how the fiber arts are unique in their ability to represent mathematical concepts. In this section, the pattern of the knitting project will be described along with how it is representing the math involved in frieze groups. The thesis will conclude with images of the final knitted product and an analysis of how knitting produces a deeper understanding of mathematical concepts

Pierce, Pamela

Mathematics

Algebra

#### Keywords

group theory, knitting, sweater, frieze patterns, wallpaper patterns, fiber arts

2021

Bachelor of Arts

#### Document Type

Senior Independent Study Thesis

COinS