Question

Relationship between curvature and radius of curvature

Answer 1

curvature is the curve of a circle

radius of curvature is the radius of that circle from which the curve is taken

Answer 2

In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof.