Radius of Curvature

The radius of curvature is given by

(1)

where is the curvature. At a given point on a curve, is the radius of the osculating circle. The symbol is sometimes used instead of to denote the radius of curvature (e.g., Lawrence 1972, p. 4).

Let and be given parametrically by

			(2)
			(3)

then

(4)

where and . Similarly, if the curve is written in the form , then the radius of curvature is given by

(5)

In polar coordinates , the radius of curvature is given by

(6)

where and (Gray 1997, p. 89).

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