Question

Set A-Spherical Images The next seven problems deal with the notion of tangent, normal, and binormal spherical images. These notions, especially that of the tangent spherical image, are very important in Chapters 3 and 5. If a(s) is a unit speed curve, then T: (a, b) -» R3 gives a curve defined by s → T(s). This curve may not be regular. Since IT(s)| 1, the image of T lies on the sphere of radius 1 about 0. This curve is called the tangent spherical image of a. We may also consider the normal spherical image N (defined by s N(s) and the binormal spherical image (defined by s- B(s)) of a.

Answer 1

"L(t) = (r cost, r sin t, h t) r^vector = dx/dt = (-r sin t, r cos t, h)