Let *P* be any point on a given curve and *Q* a neighboring point of *P* such that the arc *PQ* is concave towards its chord. Let the normals at *P* and *Q* intersect at *N*.

When *Q* → *P*, *N* tends to a definite position *C*, called the *center of curvature* of the curve at *P*. The distance *CP* is called the *radius of curvature* of the curve at the point *P* and is denoted by *ρ*. The circle with center at C and the radius *ρ*, equal to *CP*, is called the *circle of curvature* of the given curve at the point *P*. Any chord of the circle of curvature drawn through the point *P* is called the *chord of curvature*. The reciprocal of the radius of curvature is called ...

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