curvature (redirected from curvatures)

curvature

Measure of the rate of change of direction of a curved line or surface at any point. In general, it is the reciprocal of the radius of the circle or sphere of best fit to the curve or surface at that point. This notion of best fit derives from the principle that only one circle can be drawn though any three points not on the same line. The radius of curvature at the middle point is approximately equal to the radius of that one circle. This calculation becomes more exact the closer the points are. The precise value is found using a limit. Because a straight line can be thought of as an arc of a circle of infinite radius, its curvature is zero.

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curvature

1. any normal or abnormal curving of a bodily part

2. Geometry the change in inclination of a tangent to a curve over unit length of arc. For a circle or sphere it is the reciprocal of the radius

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curvature [′kər·və·chər]

(mathematics)

The reciprocal of the radius of the circle which most nearly approximates a curve at a given point; the rate of change of the unit tangent vector to a curve with respect to arc length of the curve.