Assertion: curvature's curvature | /r/HasProperty | negative
Facets:
value: at a point
type: TEMPORAL
value: everywhere
type: LOCATION
value: in anti-de sitter space
type: LOCATION
value: for convex landforms
type: TRANSITIVE-OBJECT
value: intuitively
type: MANNER
Source sentences:
text: The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of a torus.
text: If both principal curvatures are of the same sign: κ 1 κ 2 > 0 , then the Gaussian curvature is positive and the surface is said to have an elliptic point.
text: Intuitively, curvature is a positive number that describes how quickly a parametric curve is curving instantaneously.
text: This is easily visualized in the case when the curvature is a positive constant and the torsion vanishes.
text: The geodesic curvature is considered positive if the rotation of the tangent to $ \overline \gamma \; $ as one passes through $ P $ forms a right-handed screw with the direction of the normal to the surface.
text: If the principal curvatures have different signs: κ 1 κ 2 < 0 , then the Gaussian curvature is negative and the surface is said to have a hyperbolic or saddle point.
text: Because one principal curvature is negative, one is positive, and the normal curvature varies continuously if you rotate a plane orthogonal to the surface around the normal to the surface in two directions, the normal curvatures will be zero giving the asymptotic curves for that point.
text: , then the Gaussian curvature is negative and the surface is said to have a hyperbolic or saddle point.
text: Because one principal curvature is negative, one is positive, and the normal curvature varies continuously if you rotate a plane orthogonal to the surface around the normal to the surface in two directions, the normal curvatures will be zero giving the asymptotic curves for that point.
text: When cosmologists speak of the universe as being "open" or "closed", they most commonly are referring to whether the curvature is negative or positive.
text: On the other hand, when the scalar curvature is negative at a point, the volume of a small ball is larger than it would be in Euclidean space.
text: The Gaussian curvature of a strake is actually negative, hence the annular strip must be stretched—although this can be minimized by narrowing the shapes.
text: Signed curvature is either positive or negative, indicating that the curve is veering off to the right or the left, respectively.
text: Horizontal curvature can be positive, negative, or zero.
text: Vertical curvature can be positive, negative, or zero.
text: Mean curvature can be positive, negative, or zero.
text: Minimal and maximal curvatures can be positive, negative, or zero.
text: The Gaussian curvature can be positive, negative, or zero.
text: If the total curvature inside the region is negative, the strip will curl around further than necessary to close.
text: The curvature is negative, and is measured by the angle by which the curve overshoots.
text: As you have to walk uphill and downhill as well as around the post you walk farther than you would walk on flat ground showing that the curvature at that point is negative.
text: so the curvature at that point is negative.
text: In anti-de Sitter space, in the absence of matter or energy, the curvature of spacelike sections is negative, corresponding to a hyperbolic geometry, and initially parallel timelike geodesics eventually intersect.
text: , then the Gaussian curvature is positive and the surface is said to have an elliptic point.
text: When cosmologists speak of the universe as being "open" or "closed", they most commonly are referring to whether the curvature is negative or positive.
text: When the scalar curvature is positive at a point, the volume of a small ball about the point has smaller volume than a ball of the same radius in Euclidean space.
text: The curvature is taken to be positive if the curve turns in the same direction as the surface's chosen normal, and otherwise negative.
text: The sign of the curvature depends on the choice of normal: the curvature is positive if the surface curves "towards" the normal.
text: Signed curvature is either positive or negative, indicating that the curve is veering off to the right or the left, respectively.
text: If the special affine curvature is positive, then it follows that
text: In this book, we assume (unless otherwise specified) that a curvature is positive for convex landforms (eg, hills and ridges), and negative for concave ones (eg, depressions and valleys).
text: Horizontal curvature can be positive, negative, or zero.
text: Vertical curvature can be positive, negative, or zero.
text: Mean curvature can be positive, negative, or zero.
text: Minimal and maximal curvatures can be positive, negative, or zero.
text: The Gaussian curvature can be positive, negative, or zero.
text: You can verify that this is less than $\pi r^2$, and hence that the curvature of the surface of the sphere is positive, by drawing the graphs of $y=\cos x$ and $y = 1 - {x^2\over 2}$ on the same axes and showing that $\cos
text: so the curvature at that point is positive.
text: If the Gaussian curvature of a surface M is everywhere positive, then the Euler characteristic is positive