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Investigation Of Plane Symmetry In Lattice Designs
Sheridan, Katyana Sheridan, Katyana
Sheridan, Katyana
Sheridan, Katyana
Title
Investigation Of Plane Symmetry In Lattice Designs
Date
2016-12-01
Subject
abstract algebra
crystallography
frieze groups
lattice designs
plane symmetry
wallpaper groups
crystallography
frieze groups
lattice designs
plane symmetry
wallpaper groups
Material type
Collections
Files
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Sheridan_Katyana.pdf
Adobe PDF, 1.74 MB
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.
Duration
Location
Advisor
Sponsor
Course
Department
Mathematics
Degree
Bachelor of Science (BS)