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2.11 Curvature and Radius of Curvature, One of the very important aspects about the plane curve to be, studied is the degree of its bending or the concept of the curvedness of, the arc of the curve. In fact the degree of bending at different points of, the curve would be different. The characterization of the degree of, bending (or the curvedness) of a curve in the neighbourhood of a point, on a curve, is the concept of the curvature of a curve at a given point., Now we shall introduce formally the concept of the curvature of a, curve at a given point., Let P and Q be two neighbouring points on the curve C. Let, v and y + d y be the angles made by the tangents at P and Q,, respectively, with the x - axis (or the initial line)., Further, let & s be the arc length between P and Q., Y, C, Q., y + Sự, X, The angle & y through which the tangent rotates as the point of, contact moves from P to the point Q along the curve, is called the total, curvature of the arc PQ., - is called the average curvature of the arc PQ., 8s, The ratio, The limiting value of the average curvature as Q → P , (i.e. as, → 0) is called the curvature of the curve at the point P., Thus the curvature of the curve at a point P is, K = lim, ds, If the curvature K of the curve C at the point P is non zero, then, IS called the radius of curvature of the curve at P and denoted by p