<P> Augustin - Louis Cauchy defined the center of curvature C as the intersection point of two infinitely close normals to the curve, the radius of curvature as the distance from the point to C, and the curvature itself as the inverse of the radius of curvature . </P> <P> Let C be a plane curve (the precise technical assumptions are given below). The curvature of C at a point is a measure of how sensitive its tangent line is to moving the point to other nearby points . There are a number of equivalent ways that this idea can be made precise . </P> <P> One way is geometrical . It is natural to define the curvature of a straight line to be constantly zero . The curvature of a circle of radius R should be large if R is small and small if R is large . Thus the curvature of a circle is defined to be the reciprocal of the radius: </P> <Dl> <Dd> κ = 1 R . (\ displaystyle \ kappa = (\ frac (1) (R)).) </Dd> </Dl>

Curvature of a circle of radius r is given by