For a smooth space curve, the [i]curvature[/i] measures how fast the curve is bending or changing direction at a given point. The more closed is the curve, the larger is the curvature. The curvature of a line is zero.[br]The radius of curvature is the reciprocal of the curvature. It is the radius of a circle tangent to the curve that best fits at each point.

Verify that the given formula is correct for curves in the plane.