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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.
This entry comes from Encyclopædia Britannica Concise. For the full entry on curvature, visit Britannica.com.