Curvature - Wikipedia
网页In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or surface is contained in a larger space, curvature can be defined extrinsically relative to the ambient space.
CURVATURE中文(简体)翻译：剑桥词典 - Cambridge Dictionary
网页curvature. noun [ U or C ] uk / ˈkɜː.və.tʃə r/ us / ˈkɝː.və.tʃɚ /. Add to word list. the state of being curved or bent. 弯曲;曲率，曲度. the curvature of the earth's surface 地球表面的曲 …
‘弯’的度量 - 曲率 - 知乎 - 知乎专栏
网页实际上，对于曲面，我们经常会用主曲率（principal curvatures）, 衡量了在给定点一个曲面在这一点的不同方向怎样不同弯曲的程度。 在曲面上取一点E，曲面在E点的法线为N轴，过N轴可以有无限多个剖切平面，每个剖切平面与曲面相交，其交线为一条平面曲线，每 ...
曲率 - 維基百科，自由的百科全書
网页曲線 C 在 P 點的密切圓和曲率半徑. 曲率有多種等價的定義. 圓上每一點處的彎曲程度都相同，半徑越小彎曲得越厲害，所以可以用半徑的倒數來定量描述圓的彎曲程度。. 直線可以看作半徑無限大的圓，所以直線的曲率為0。. 對於任意形狀的曲線，每一點處的 ...
Curvature | Riemannian, Non-Euclidean & Manifolds | Britannica
网页2024年9月3日 · Curvature, in mathematics, the rate of change of direction of a curve with respect to distance along the curve. At every point on a circle, the curvature is the reciprocal of the radius; for other curves (and straight lines, which can be regarded as circles of infinite radius), the curvature is the.
Curvature - Encyclopedia of Mathematics
网页2020年6月5日 · Curvature. A collective term for a series of quantitative characteristics (in terms of numbers, vectors, tensors) describing the degree to which some object (a curve, a surface, a Riemannian space, etc.) deviates in its properties from certain other objects (a straight line, a plane, a Euclidean space, etc.) which are considered to be flat.
Curvature -- from Wolfram MathWorld
网页2024年8月22日 · The curvature at a point on a surface takes on a variety of values as the plane through the normal varies. As varies, it achieves a minimum and a maximum (which are in perpendicular directions) known as the principal curvatures.
Calculus III - Curvature - Pauls Online Math Notes
网页2022年11月16日 · The curvature measures how fast a curve is changing direction at a given point. There are several formulas for determining the curvature for a curve. The formal definition of curvature is, κ = ∥∥ ∥d →T ds ∥∥ ∥ κ = ‖ d T → d s ‖. where →T T → is the unit tangent and s s is the arc length.
Curvature | Calculus III - Lumen Learning
网页Explain the meaning of the curvature of a curve in space and state its formula. An important topic related to arc length is curvature. The concept of curvature provides a way to measure how sharply a smooth curve turns. A circle has constant curvature. The smaller the radius of the circle, the greater the curvature.
What Is Curvature? - SpringerLink
网页2019年1月3日 · The curvature of a surface in space is described by two numbers at each point, called the principal curvatures. We will define them formally in Chapter 8, but here is an informal recipe for computing them. Suppose S is a surface in \ (\mathbb {R}^3\), p is a point in S, and N is a unit normal vector to S at p. 1.