Date of Award
Yun Myung Oh, Ph.D.
The structure of helix is a significant field in the differential geometry studies, and it is profoundly studied and still studied over the period. A curve of constant slope or general helix is defined by the property that its tangent vector field makes a constant angle with a fixed straight line (the axis of the general helix) in Euclidean space.
A prevalent result stated by M.A. Lancret in 1802 and first proved by B. de Saint Venant in 1845 is: A necessary and sufficient condition that a curve be a general helix is that the ratio of curvature to torsion be constant. Now we know that a general helix has a constant ratio of curvature to torsion, it can be further studied by considering different relationship between curvature and torsion. The purpose of this study is to investigate the behavior of the helix when the ratio of curvature to torsion is a linear function.
Lim Seo, Ye, "The Geometry of Curves" (2014). Posters, Presentations, and Papers. 18.