- #1
ltkach2015
- 37
- 1
Hello
I am interested in the Frenet-Serret Formulas (theory of curves?) relationship to theory of surfaces.
1) Can one arrive to the Frenet-Serret Formulas starting from the theory of surfaces? Any advice on where to begin?
2) For a surface that contain a space curve: if the unit tangent vector to the curve is the very same unit tangent vector the surface then why/how is the unit normal vector to the curve not in the same direction as the surface's gradient vector?
Thank you
I am interested in the Frenet-Serret Formulas (theory of curves?) relationship to theory of surfaces.
1) Can one arrive to the Frenet-Serret Formulas starting from the theory of surfaces? Any advice on where to begin?
2) For a surface that contain a space curve: if the unit tangent vector to the curve is the very same unit tangent vector the surface then why/how is the unit normal vector to the curve not in the same direction as the surface's gradient vector?
Thank you