The osculating circle
In the interactive figure, drag point P along the curve from point A to point B. The principal unit normal vector is always perpendicular to the unit tangent vector , and always points towards the center of curvature C. The circle centered at C and passing through point P shares the same tangent line to the curve at point P.
Drag points A and B, as well as the three control points on the curve to explore different paths.
Developed for use with Thomas' Calculus, published by Pearson.