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curvature    音标拼音: [k'ɚvətʃɚ]
n. 屈曲,弯曲,曲率

屈曲,弯曲,曲率

curvature
曲率

curvature
曲率

curvature
n 1: (medicine) a curving or bending; often abnormal; "curvature
of the spine"
2: the rate of change (at a point) of the angle between a curve
and a tangent to the curve
3: the property possessed by the curving of a line or surface
[synonym: {curvature}, {curve}]

Curvature \Cur"va*ture\ (k?r"v?-t?r; 135), n. [L. curvatura. See
{Curvate}.]
1. The act of curving, or the state of being bent or curved;
a curving or bending, normal or abnormal, as of a line or
surface from a rectilinear direction; a bend; a curve.
--Cowper.
[1913 Webster]

The elegant curvature of their fronds. --Darwin.
[1913 Webster]

2. (Math.) The amount of degree of bending of a mathematical
curve, or the tendency at any point to depart from a
tangent drawn to the curve at that point.
[1913 Webster]

{Aberrancy of curvature} (Geom.), the deviation of a curve
from a circular form.

{Absolute curvature}. See under {Absolute}.

{Angle of curvature} (Geom.), one that expresses the amount
of curvature of a curve.

{Chord of curvature}. See under {Chord}.

{Circle of curvature}. See {Osculating circle of a curve},
under {Circle}.

{Curvature of the spine} (Med.), an abnormal curving of the
spine, especially in a lateral direction.

{Radius of curvature}, the radius of the circle of curvature,
or osculatory circle, at any point of a curve.
[1913 Webster]


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  • 如何简明地解释曲率(curvature)?
    这个事实告诉我们,可以用密切圆的曲率来定义曲线的曲率(因为格式所限,详细推导请查看 此处,还是挺有意思的,综合应用了线性代数的知识): 已知函数 在 点有二阶导数 ,且 ,则此点有密切圆,其半径为: 此时,曲线的 曲率 也就是密切圆的曲率,为: 所以密切圆也称为曲线的 曲率圆
  • 如何简明地解释曲率(curvature)? - 知乎
    一个圆半径越小,看起来就越弯曲;半径越大,看起来就越平,半径趋于无穷大,圆看起来就像一条直线,就几乎不弯曲了。所以我们把圆的半径的倒数,定义为曲率,因为我们希望曲率是一个衡量几何体弯曲程度的量。 对于一般的曲线,每点局部可以近似看成一小段圆弧(可以看其他答主提到的
  • differential geometry - Understanding the formula for curvature . . .
    For this reason, curvature requires differentiating T (t) with respect to arc length, S (t), instead of the parameter t" I feel this is not a sufficient explanation and more explanation is needed to clarify the formula As it just states a reason that 'the curvature should related to the arclength (geometrical quantity) rather than velocity or
  • 如何简明地解释曲率(curvature)? - 知乎
    来自本材料得图片不做另外介绍 6 1 3 Definition of Curvature 曲率 (Curvature)是衡量曲线陡峭程度的量 (quantity that measures the sharpness of a curve),与加速度密切相关 (closely related to the acceleration)。 想象一下,你正沿着弯曲的道路驾驶汽车。
  • differential geometry - Curvature Formula Proof By Definition . . .
    Curvature Formula Proof By Definition Ask Question Asked 5 years, 11 months ago Modified 5 years, 11 months ago
  • differential geometry - Radius of Curvature when dy dx is undefined . . .
    @JoonasD6, the radius of curvature is a geometric invariant that can be thought of as the radius of the osculating circle at the point Alternatively, it is the length of the second derivative with respect to an arc length parametrisation
  • Is there any easy way to understand the definition of Gaussian Curvature?
    The Gaussian curvature is the ratio of the solid angle subtended by the normal projection of a small patch divided by the area of that patch The fact that this ratio is based totally on the definition of distance within the surface (independent of the embedding of the surface; that is, bending and twisting, etc ) is Gauss' Theorema Egregium
  • Intrinsic and Extrinsic curvature - Mathematics Stack Exchange
    I want to understand the basic conceptual idea about intrinsic and extrinsic curvature If we consider a plane sheet of paper (whose intrinsic curvature is zero) rolled into a cylindrical shape, th
  • differential geometry - Holonomy is curvature - but how is curvature . . .
    The way I think about this result is that once you know the connection and curvature forms, you can do an integration and compute the holonomy I think there must be a way to reverse this formula and compute the curvature from the holonomy Informally, one ought to be able to take a derivative and compute $\Omega$





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