Differential Geometry | Topology Answers

Find

the Curvature and

torsion of the Curves r = (u, (1 + u)/u, (1 - u ^ 2)/u)

Suppose

u=rcos(wt)i+rsin(wt)j where r and w are constants, find the vector velocity

Find the curvature, the radius and the center of curvature at a point.

r = sin 3 theta , theta = 0

Find the curvature, the radius and the center of curvature at a point.

x=t, y=1/t ; t=1

Find the curvature, the radius and the center of curvature at a point.

x = t ^ 2 , y = t ^ 3 ; t = 1/2

Find the curvature, the radius and the center of curvature at a point.

y=sin x, x = pi/2

Find the curvature, the radius of curvature and the center of curvature having a parametric equations at the given point:

r = 4cos 2theta , theta = 1/12 * pi

Find the curvature, the radius of curvature and the center of curvature having a parametric equations at the given point:

y=e^x , (0,1)

Find the curvature, the radius of curvature and the center of curvature having a parametric equations at the given point:

x = 3t ^ 2 , y = t ^ 3 - 3t at t = 2

if two families of geodesics surface intersect at a constant angle, prove that the surface has zero gaussian curvature.