osculating circles in vector calculus

These Maple worksheets illustrate various aspects of osculating circles and the TNB triad of vectors alomg a spacecurve.

• oscircle.mw
  osculating circle on the graph of a function in the plane: parabola at the origin. Explore zoom in.
• osculate-parabola.mw
  visualizing the osculating circle along the parabola, and its evolute of centers of those circles.
• osculate-ellipse.mw
  animation of the evolute of an ellipse and its osculating circles, with Explore zoom in at one vertex.
  [derivation of formulas: osculate-ellipse-derivation.mw]
• osculating_circle_helix.mw
  osculating circle and TNB frame etc along helix. animation of all the TNB vectors and the osculating plane and circle, normal plane.
• osculating_circle_tcubic.mw
  twisted cubic osculating circle. Animation of osculating circles and Explore zoom in at the origin.