The radius of curvature is the radius of an approximating circle passing through points on the curve. The radius of the approximate circle at a particular point is the radius of curvature . The curvature vector length is the radius of curvature . The radius changes as the curve moves. Denoted by R, the radius of curvature is found out by the following formula. Formula for Radius of Curvature Definition 1.3.1 The circle which best approximates a given curve near a given point is called the circle of curvature or the osculating circle2 at the point. The radius of the circle of curvature is called the radius of curvature at the point and is normally denoted \ (\rho\text {.}\) The curvature at the point is \ (\kappa=\frac {1} {\rho}\text {.}\) The centre of the circle of curvature is called centre of curvature at the point. Curvature and Radius of Curvature Curvature (symbol, $\kappa$) is the mathematical expression of how much a curve actually curved. It is the measure of the average change in direction of the curve per unit of arc.
