with(plots): with(linalg): frenet.m contains the functions kappa, tau, tang, normalv, and binor as described in the appendix of O'Neills book. You will need to download this from my web page or make your own file (as described in O'Neill). Replace "/Users/shelly/Maple/frenet.m" with the location where you saved frenet.m. read "/Users/shelly/Maple/frenet.m"; c := t -> [cos(t),sin(t),t/5]; tang(c)(t), normalv(c)(t), binor(c)(t); spacecurve(c(t),t=0..4*Pi, scaling=constrained); animate(spacecurve,[c(a*t),t=0..4*Pi], a=0..1, numpoints=1000, thickness=3); C1 := spacecurve(c(t),t=0..4*Pi, color=black,numpoints=1000, thickness=3); Tangv := animate(spacecurve,[matadd(c(a),scalarmul(tang(c)(a),t)),t=0..1], a=0..4*Pi, numpoints=1000, color=red, thickness=3, frames=50); Normalv := animate(spacecurve,[matadd(c(a),scalarmul(normalv(c)(a),t)),t=0..1], a=0..4*Pi, numpoints=1000, color=blue, thickness=3, frames=50); Binormv := animate(spacecurve,[matadd(c(a),scalarmul(binor(c)(a),t)),t=0..1], a=0..4*Pi, numpoints=1000, color=green, thickness=3, frames=50); display({C1,Tangv, Normalv, Binormv}, scaling=constrained);