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Statements

Subject Item
dbr:Total_curvature
rdf:type
yago:Abstraction100002137 yago:Shape100027807 yago:WikicatCurves yago:Line113863771 yago:Curve113867641 yago:Attribute100024264
rdfs:label
Варіація повороту кривої Total curvature Totalkrümmung 总曲率
rdfs:comment
在数学中的曲线微分几何的研究中，一个浸入在平面上的曲线的总曲率是曲率的曲线积分： 闭曲线的总曲率是 2π 的整数倍，该整数称为曲线的指数或转数。其中转数是单位切向量关于起点的绕数，或者等价的高斯映射的次数。局部不变量曲率和整体拓扑不变量指数的关系是高维黎曼几何的代表性结果，如高斯－博內定理。 Варіація повороту кривої — інтеграл кривини кривої за її довжиною. In der Kurventheorie, einem Teilgebiet der Mathematik, wird die Totalkrümmung einer Kurve definiert als das Integral ihrer Krümmung , also als . In mathematical study of the differential geometry of curves, the total curvature of an immersed plane curve is the integral of curvature along a curve taken with respect to arc length: The total curvature of a closed curve is always an integer multiple of 2π, called the index of the curve, or turning number – it is the winding number of the unit tangent vector about the origin, or equivalently the degree of the map to the unit circle assigning to each point of the curve, the unit velocity vector at that point. This map is similar to the Gauss map for surfaces.
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dbc:Curves dbc:Curvature_(mathematics)
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1117702739
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n4:Winding_Number_Around_Point.svg?width=300
dbo:abstract
In mathematical study of the differential geometry of curves, the total curvature of an immersed plane curve is the integral of curvature along a curve taken with respect to arc length: The total curvature of a closed curve is always an integer multiple of 2π, called the index of the curve, or turning number – it is the winding number of the unit tangent vector about the origin, or equivalently the degree of the map to the unit circle assigning to each point of the curve, the unit velocity vector at that point. This map is similar to the Gauss map for surfaces. Варіація повороту кривої — інтеграл кривини кривої за її довжиною. In der Kurventheorie, einem Teilgebiet der Mathematik, wird die Totalkrümmung einer Kurve definiert als das Integral ihrer Krümmung , also als . 在数学中的曲线微分几何的研究中，一个浸入在平面上的曲线的总曲率是曲率的曲线积分： 闭曲线的总曲率是 2π 的整数倍，该整数称为曲线的指数或转数。其中转数是单位切向量关于起点的绕数，或者等价的高斯映射的次数。局部不变量曲率和整体拓扑不变量指数的关系是高维黎曼几何的代表性结果，如高斯－博內定理。
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wikipedia-en:Total_curvature?oldid=1117702739&ns=0
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wikipedia-en:Total_curvature