## 3

## Curvature

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 intersects 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 the ...

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