P-38 Some Characterizations of Involute Curves in Euclidean and Minkowski 3-Space
Presenter Status
Student, Physics
Second Presenter Status
Professor, Mathematics
Preferred Session
Poster Session
Location
Buller Hall Hallways
Start Date
21-10-2022 2:00 PM
End Date
21-10-2022 3:00 PM
Presentation Abstract
The involute of a space curve is a curve whose tangent vector is orthogonal to the tangent vector of another curve. In this work, we are interested in constructing a framework to further study the involute of curves in Euclidean and Minkowski three-space. Our framework relies on the curvature and ratio of torsion-to-curvature of a curve to study the involute. In classical differential geometry, a space curve is described by its curvature and torsion, and the ratio of torsion-to-curvature is an approach to classify curves. Using the ratio of torsion-to-curvature instead of the torsion is a more intuitive approach because it shows the dependence of the involute’s Frenet-Serret apparatus on the nature of the original curve. We provide new insights on the involute of slant helices through our framework and provide future directions for our work.
P-38 Some Characterizations of Involute Curves in Euclidean and Minkowski 3-Space
Buller Hall Hallways
The involute of a space curve is a curve whose tangent vector is orthogonal to the tangent vector of another curve. In this work, we are interested in constructing a framework to further study the involute of curves in Euclidean and Minkowski three-space. Our framework relies on the curvature and ratio of torsion-to-curvature of a curve to study the involute. In classical differential geometry, a space curve is described by its curvature and torsion, and the ratio of torsion-to-curvature is an approach to classify curves. Using the ratio of torsion-to-curvature instead of the torsion is a more intuitive approach because it shows the dependence of the involute’s Frenet-Serret apparatus on the nature of the original curve. We provide new insights on the involute of slant helices through our framework and provide future directions for our work.
Acknowledgments
Fall 2022 Undergraduate Research Scholar Award