curvature animation

Sun, 2015-03-08 21:18

The "circles of curvature" of the curve with polar equation r = sin θ -0.5cos 3 θ.

curvature applet

Wed, 2007-10-31 20:15

I wrote this applet for my Calculus I students to investigate, very preliminarily, the curvature of y=x2 at the origin. Notice how the circle is in contact with two points of the parabola until the radius gets small enough, and then it just sits on the origin. Hmmm: what does that tell us?