In differential geometry, the reciprocal of curvature is the radius of curvature, ie R = 1/K. The curvature of a plane curve is the rate of rotation of the tangential direction angle to the arc length for a point on the curve, defined by differentiation, indicating the extent to which the curve deviates from the line. For a curve, it is equal to the radius of the arc closest to the curve at that point. For surfaces, the radius of curvature is the radius of the circle that best fits the normal section or a combination thereof.
Half circle
For a semicircle of radius a of the upper half plane:
For a semicircle of radius a of the upper half plane:
The radius of curvature of the circle of radius a is equal to a.
oval
In an ellipse having a major axis 2a and a minor axis 2b, the apex on the major axis has a minimum radius of curvature of any point;
And the vertices on the short axis have the maximum radius of curvature of any point.
