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.
Plücker's conoid Hyperbolic paraboloid Darboux frame Unit cylinder Pancake curve
Birincil Dil | İngilizce |
---|---|
Konular | Diferansiyel ve İntegral Denklemlerin Sayısal Çözümü |
Bölüm | Natural Sciences |
Yazarlar | |
Yayımlanma Tarihi | 30 Eylül 2024 |
Gönderilme Tarihi | 28 Şubat 2024 |
Kabul Tarihi | 12 Eylül 2024 |
Yayımlandığı Sayı | Yıl 2024 |