Question

Reciprocal of curvature of curve at any point is reffered as

Answer 1

Step-by-step explanation:

At the displacement Δs along the arc of the curve, the point M moves to the point M1. The position of the tangent line also changes: the angle of inclination of the tangent to the positive x−axis at the point M1 will be α+Δα. Thus, as the point moves by the distance Δs, the tangent rotates by the angle Δα. (The angle α is supposed to be increasing when rotating counterclockwise.)

The absolute value of the ratio ΔαΔs is called the mean curvature of the arc MM1. In the limit as Δs→0, we obtain the curvature of the curve at the point M:

K=limΔs→0∣∣∣ΔαΔs∣∣∣.

From this definition it follows that the curvature at a point of a curve characterizes the speed of rotation of the tangent of the curve at this point.

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