Math 425 homework 4 2024 - Study guides, Class notes & Summaries

Question 1 (15 points). Show the following curve is a Frenet curve. Find the curvature and torsion of this curve. √ γ(t) =< t + cos(t), t − cos(t), 2t > Question 2 (10 points). Let γ : [a, b] → R3 be a Frenet curve. Show that d2s ds 2 a(t) = dt2 T(s(t)) + ( dt ) κ(s(t))N(s(t)). Here s(t) = t ǁγ′(t)ǁdt and a(t) = γ′′(t). Question 3 (30points). Let the image of the curve r : [0, l] R3 be on the sphere of radius R and centered at origin. Assume this curve is para...