Date of Graduation
5-2023
Document Type
Thesis
Degree Name
Bachelor of Science
Degree Level
Undergraduate
Department
Mathematical Sciences
Advisor/Mentor
Harriss, Edmund
Committee Member/Reader
Warren, Ron
Committee Member/Second Reader
Van Horn-Morris, Jeremy
Committee Member/Third Reader
Youngblood, Joshua
Abstract
A frame defines a basis at a point in R^n, and we can frame a curve by placing one at every point along it. This thesis investigates adapted framed curves in R^2 and R^3 in which they are used to provide information about how a curve twists and turns. We derive differential information from the frames that describe how they change and consequently how the curve changes. We also deduce special properties of each framing and discuss how the differential information suffices to describe the shape of curves.
Keywords
framed curve, Darboux frame, Frenet frame, parallel transport frame
Citation
Sattler, M. (2023). Framing How We Think About Curves. Mathematical Sciences Undergraduate Honors Theses Retrieved from https://scholarworks.uark.edu/mascuht/6