circle of curvature

The osculating circle of a curve C at a given point P is the circle that has the same tangent as C at point P as well as the same curvature. Just as the tangent line is the line best approximating a curve at a point P, the osculating circle is the best circle that approximates the curve at P. Ignoring degenerate curves such as straight lines, the osculating circle of a given curve at a given point is unique.

curvature | evolute | osculating curves | radius of curvature | tangent