Circle of Curvature

x coordinate of point

change curve

The circle of curvature is a visual expression of the curvature of a curve at a given point. The circle of curvature, or osculating circle, of a curve at a point is the circle tangent to the curve with the same curvature. This Demonstration shows the circles of curvature along several curves.

For a nice animation, run the two sliders simultaneously in the back and forth mode.