Question

short notes on centre of curvature

Answer 1

Definition of center of curvature

: the center of the circle whose center lies on the concave side of a curve on the normal to a given point of the curve and whose radius is equal to the radius of curvature at that point

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Answer 2

the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal vector. It is the point at infinity if the curvature is zero. The osculating circle to the curve is centered at the centre of curvature. Cauchy defined the center of curvature C as the intersection point of two infinitely close normal lines to the curve. The locus of centers of curvature for each point on the curve comprise the evoluteof the curve. This term is generally used in Physics regarding to study of the lenses.