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.