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In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object such as a surface deviates from being a flat plane, or a curve from being straight as in the case of a line, but this is defined in different ways depending on the context. There is a key distinction between extrinsic curvature, which is defined for objects embedded in another space ? in a way that relates to the radius of curvature of circles that touch the object ?, and intrinsic curvature, which is defined at each point in a Riemannian manifold. This article deals primarily with the first concept.