“Asymptomatic” vs. “Asymptotic” vs. “Asystematic”: Is There A Difference?

SOLVED:Let αbe an asymptotic curve in M ⊂𝐑^3 with curvature κ>0. (a) Prove that the binormal B of αis normal to the surface along α, and deduce that S(T)=τN. (b) Show that along αthe surface has Gaussian curvature K=-τ^2. (c) Use (b) to find the Gaussian curvature of the helicoid (Ex. 4.3).