Curvature is the rotation rate of the tangent direction angle of a point on a curve to the arc length, which is defined by differential and represents the degree to which the curve deviates from a straight line. A numerical value that mathematically represents the degree of curvature of a curve at a certain point. The greater the curvature, the greater the curvature of the curve. The reciprocal of curvature is the radius of curvature.
The reciprocal of curvature is the radius of curvature, that is, r =1/k.
The curvature of a plane curve is defined by the differential of the rotation rate of the tangent direction angle to the arc length at a certain point on the curve, which indicates the degree to which the curve deviates from the straight 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 is most suitable for the normal section or its combination. The larger the radius of a circle, the smaller the degree of bending, and the closer it is to a straight line. So the larger the radius of curvature, the smaller the curvature, and vice versa.