Poster Title
P-36 Exploring 2nd Natural Mates and Families of Primitive Curves
Department
Mathematics
Abstract
The natural mate of a unit speed curve is generated by letting its principal normal vector be the tangent vector of the new curve. Expanding on Deshmukh et al., we demonstrate that given a curve, the primitive curve of which it is the natural mate is not uniquely determined, giving a family of curves with the same natural mate. We then explore the 2nd natural mate, demonstrating a simple relationship between its curvature and torsion, and proving several smaller theorems regarding how constraints on the primitive, 1st natural mate, and 2nd natural mate may constrain the other curves.
Location
Buller Hall 207
Start Date
3-11-2022 1:30 PM
End Date
3-11-2022 3:30 PM
P-36 Exploring 2nd Natural Mates and Families of Primitive Curves
Buller Hall 207
The natural mate of a unit speed curve is generated by letting its principal normal vector be the tangent vector of the new curve. Expanding on Deshmukh et al., we demonstrate that given a curve, the primitive curve of which it is the natural mate is not uniquely determined, giving a family of curves with the same natural mate. We then explore the 2nd natural mate, demonstrating a simple relationship between its curvature and torsion, and proving several smaller theorems regarding how constraints on the primitive, 1st natural mate, and 2nd natural mate may constrain the other curves.