Assertion: curvature's curvature | /r/HasProperty | equal
Facets:
value: to the reciprocal
type: OTHER
value: to zero
type: OTHER
value: to minimum curvature
type: OTHER
value: in this case
type: OTHER
value: to κ(0
type: OTHER
value: of a circle
type: OTHER
value: everywhere
type: LOCATION
value: to the given function
type: OTHER
value: to the length of $ \overline{c}\
type: OTHER
value: to $ k
type: OTHER
value: to the curvature of the curve
type: OTHER
value: at umbilic points
type: LOCATION
value: to 4π times
type: TEMPORAL
value: to 2/r2
type: OTHER
Source sentences:
text: The Gaussian curvature, named after Carl Friedrich Gauss, is equal to the product of the principal curvatures, k 1 k 2 .
text: The average curvature of the arc of a circle is equal to the reciprocal of the circle’s radius and thus gives an intuitive characterization of the degree of curvature of a circle: the arc’s curvature increases with decreasing radius.
text: If, for example, the total curvature is equal to zero at all points of the surface, then each sufficiently small piece of the surface is applicable to a plane.
text: For example, the scalar curvature of the 2-sphere of radius r is equal to 2/r2.
text: For a closed Riemannian 2-manifold M, the scalar curvature has a clear relation to the topology of M, expressed by the Gauss–Bonnet theorem: the total scalar curvature of M is equal to 4π times the Euler characteristic of M.
text: At umbilic points , both principal curvatures are equal and every tangent vector can be considered a principal direction.
text: f {\displaystyle H_{f}} ; the two curvatures are equal to the reciprocal of the droplet's radius
text: The curvature of the curve is equal to the absolute value of the vector
text: The normal curvature is equal to the curvature of the curve $ \gamma _ {
text: In this case the scalar curvature is equal to $ K $.
text: In the regular case the total curvature is equal to the integral of the Gaussian curvature.
text: The total curvature of $ C $ is equal to the length of $ \overline{C}\; $.
text: R, there exists a curve β whose first and second derivatives are linearly independent, such that the special affine curvature of β relative to the special affine parameterization is equal to the given function k.
text: The computed curvature is equal to (Minimum curvature + Maximum curvature)
text: We will find that this definition leads directly to the result that the curvature, K, of a circle is equal to the reciprocal of its radius
text: The curvature of a circle is constant and is equal to the reciprocal of the radius.
text: The average curvature of the arc of a circle is equal to the reciprocal of the circle’s radius and thus gives an intuitive characterization of the degree of curvature of a circle: the arc’s curvature increases with decreasing radius.
text: If, for example, the total curvature is equal to zero at all points of the surface, then each sufficiently small piece of the surface is applicable to a plane.
text: A sphere of radius R has constant Gaussian curvature which is equal to 1/R2.
text: The projection of the curve onto this plane has the form: This is a parabola up to terms of order ( ), whose curvature at 0 is equal to κ(0).
text: In the category of Riemannian manifolds, one can consider the sectional curvature of the manifold and require that this curvature be everywhere less than or equal to zero.