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- Curvature abstract "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 deviates from being flat, or straight 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 (usually a Euclidean 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.The canonical example of extrinsic curvature is that of a circle, which everywhere has curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The curvature of a smooth curve is defined as the curvature of its osculating circle at each point.More commonly this is a scalar quantity, but one may also define a curvature vector that takes into account the direction of the bend as well as its sharpness. The curvature of more complex objects (such as surfaces or even curved n-dimensional spaces) is described by more complex objects from linear algebra, such as the general Riemann curvature tensor.The remainder of this article discusses, from a mathematical perspective, some geometric examples of curvature: the curvature of a curve embedded in a plane and the curvature of a surface in Euclidean space.See the links below for further reading.".
- Curvature thumbnail Osculating_circle.svg?width=300.
- Curvature wikiPageExternalLink CurvatureAndTorsionOfCurves.mw.
- Curvature wikiPageExternalLink 5-03.htm.
- Curvature wikiPageExternalLink k.htm.
- Curvature wikiPageID "60770".
- Curvature wikiPageRevisionID "603814340".
- Curvature direction "vertical".
- Curvature first "D.D.".
- Curvature footer "Animations of the signed curvature and the acceleration vector".
- Curvature hasPhotoCollection Curvature.
- Curvature id "Curvature".
- Curvature image "Lemniscate_nebeneinander_animated.gif".
- Curvature image "Lissajous-Curve_nebeneinander_animated.gif".
- Curvature last "Sokolov".
- Curvature oldid "12026".
- Curvature title "Curvature".
- Curvature width "260".
- Curvature subject Category:Curvature_(mathematics).
- Curvature subject Category:Multivariable_calculus.
- Curvature comment "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 deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context.".
- Curvature label "Courbure".
- Curvature label "Curvatura".
- Curvature label "Curvatura".
- Curvature label "Curvatura".
- Curvature label "Curvature".
- Curvature label "Kromming (meetkunde)".
- Curvature label "Krzywizna krzywej".
- Curvature label "Krümmung".
- Curvature label "Кривизна".
- Curvature label "انحناء".
- Curvature label "曲率".
- Curvature label "曲率".
- Curvature sameAs Krümmung.
- Curvature sameAs Curvatura.
- Curvature sameAs Courbure.
- Curvature sameAs Curvatura.
- Curvature sameAs 曲率.
- Curvature sameAs 곡률.
- Curvature sameAs Kromming_(meetkunde).
- Curvature sameAs Krzywizna_krzywej.
- Curvature sameAs Curvatura.
- Curvature sameAs m.0ghlg.
- Curvature sameAs Q214881.
- Curvature sameAs Q214881.
- Curvature wasDerivedFrom Curvature?oldid=603814340.
- Curvature depiction Osculating_circle.svg.
- Curvature isPrimaryTopicOf Curvature.
