Date of Award
9-1-2020
Degree Name
Master of Science
Department
Mathematics
First Advisor
Kocik, Jerzy
Abstract
The present study focuses on developing a Frenet-Serret frame and the Apollonian Window. In the first part of the study Apollonian disks are generated for first four generations by developing visual basic codes in excel. For the second part of the study, three orthonormal basis vectors, namely, tangent, normal, and binormal vectors have been calculated for the tangent points of Apollonian discs for the first three generations. Equations of the Normal, Osculating and Rectifying planes and Taylor Series approximation have been calculated for specific theta. Because Apollonian Window consists of planar curves with constant curvature, torsion is nowhere present. The planar Frenet-Serret Equations for the first three generations for the Apollonian Window is also shown.
Access
This thesis is Open Access and may be downloaded by anyone.