In this paper, we focus on a rare curve, “The pancake curve” which was named by Robert Ferréol. We investigate the Darboux frame of the curve, and we calculate the curvatures: geodesic curvature, normal curvature, and geodesic torsion. We discuss two cases, for instance, pancake curve as an intersection of Plücker’s conoid and unit cylinder, and the intersection of a hyperbolic paraboloid and unit cylinder. Moreover, we give the relations between the Frenet and Darboux curvatures. Finally, we give some examples related to the Frenet and Darboux frame and curvatures.
Primary Language | English |
---|---|
Subjects | Numerical Solution of Differential and Integral Equations |
Journal Section | Natural Sciences |
Authors | |
Publication Date | September 30, 2024 |
Submission Date | February 28, 2024 |
Acceptance Date | September 12, 2024 |
Published in Issue | Year 2024 |