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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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  • differential geometry - Understanding the formula for curvature . . .
    A way to define curvature then would be to find the "tangent circle" (if it exists) at each point, then the curvature would be the reciprocal of the radius of this "tangent circle" It turns out that the equations needed to derive the tangent circle are simplified if the tangent vector at each point of the curve has length $1$ , which is the
  • Is there any easy way to understand the definition of Gaussian Curvature?
    If you take that sheet and bend it or roll it up into a tube or twist it into a cone, its Gaussian curvature stays zero Indeed, since paper isn't particularly elastic, pretty much anything you can do to the sheet that still lets you flatten it back into a flat sheet without wrinkles or tears will preserve its Gaussian curvature
  • calculus - Why is the radius of curvature = 1 (curvature . . .
    My textbook Thomas' Calculus (14th edition) initially defines curvature as the magnitude of change of direction of tangent with respect to the arc length of the curve (|dT ds|, where T is the tangent vector and s is the arc length) and later by intuition conclude that κ = 1 ρ (where, κ=curvature,ρ = radius)
  • 如何简明地解释曲率（curvature）？ - 知乎
    如何简明地解释曲率（curvature）？ 曲率是啥，挠率（torsion）是啥，咋来的，有啥用？ 指的是对于函数 [公式] 显示全部
  • How to know when a curve has maximum curvature and why?
    The curvature is what makes the difference between a straight line and a curve, i e a measure of "non-straightness" And it is intuitive that a curve of constant curvature is a circle For curves that are not circles, the curvature must be defined locally, i e it varies from place to place
  • Deriving curvature formula - Mathematics Stack Exchange
    $\begingroup$ Sure, but ${\bf T}' = \kappa {\bf N}$ there means ${\bf T}'(s) = \kappa(s) {\bf N}(s)$ and so curvature is defined in terms of arc length It sounds to me like he is asking for a derivation divorced from arc length, but maybe I am hearing him wrong $\endgroup$
  • differential geometry - What the curvature $2$-form really represents . . .
    I mean, when we define curvature for curves on space, the curvature is meant to represent how much the curve deviates from a straight line On the other hand, when reading books about General Relativity some time ago, I read that the curvature of the Levi-Civita connection is intended to encode the information of the difference between a
  • Intrinsic and Extrinsic curvature - Mathematics Stack Exchange
    The best way I have had it put to me is that, extrinsic curvature corresponds to everyone's layman understanding of curvature before we were ever introduced to differential geometry If the difference in dimension (or co-dimension) is greater than one, we can define multiple normal vectors to the manifold $\Sigma$, and there is a third notion
  • differential geometry - Intuitive definition for curvature . . .
    This acceleration is directed towards the center of curvature of the curve For instance, if you are travelling on a circular road, then you are constantly accelerating towards the center of the circle The curvature $\kappa$ of a curve at a point is the magnitude of this acceleration when you are travelling at unit speed
  • Difference between second order derivative and curvature.
    The curvature is then defined as the inverse of the radius of curvature So a large radius of curvature indicates a graph is nearly flat This means the curvature, as the inverse of the radius of curvature, would be nearly zero for a line that is nearly straight The more curled a graph is, the higher it's curvature value





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