the circle that best approximates the curve at a point. More precisely, given a point on a curve, every other point of the curve defines a circle (or sometimes a line) passing through and tangent to the curve at . The osculating circle is the limit, if it exists, of this circle when tends to . Then the center of curvature and the radius of curvature of the curve at are the center and the radius of the osculating circle.

The radius of