curvature - meaning and definition. What is curvature
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What (who) is curvature - definition

INVERSE OF THE RADIUS OF CURVATURE
Flat space; Curvature of space; Intrinsic curvature; First curvature; Space curvature; Curvature (plane curve); Curvature (space curve); Curvature (mathematics); Extrinsic curvature; Negative curvature; Positive curvature; Curvatures; Curvature of curves on surfaces; Curvature of space curves; Curvature of plane curves; Curvature of surfaces; Surface curvature; Concave curve; Signed curvature
  • A migrating wild-type ''[[Dictyostelium discoideum]]'' cell whose boundary is colored by curvature. Scale bar: 5 µm.
  • Curvature comb
  • '''N'''}}. The curvature describes the rate of rotation of the frame.
  • [[Saddle surface]] with normal planes in directions of principal curvatures
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  • Moving a vector along a curve from A → N → B → A produces another vector. The inability to return to the initial vector is measured by the holonomy of the surface. In a space with no curvature, the angle α is 0 degrees, and in a space with curvature, the angle α is greater than 0 degrees. The more space is curved, the greater the magnitude of the angle α.
  • '''T'''′(''s'')}}

curvature         
n.
1.
Bending, bend, flexure, crook, curvity, curve, incurvation, arcuation.
2.
Rate of curvature or inflection.
curvature         
The curvature of something is its curved shape, especially when this shape is part of the circumference of a circle. (TECHNICAL)
...the curvature of the earth...
N-UNCOUNT: oft N of n
Curvature         
·noun 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.
II. Curvature ·noun 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.

Wikipedia

Curvature

In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.

For curves, the canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The curvature at a point of a differentiable curve is the curvature of its osculating circle, that is the circle that best approximates the curve near this point. The curvature of a straight line is zero. In contrast to the tangent, which is a vector quantity, the curvature at a point is typically a scalar quantity, that is, it is expressed by a single real number.

For surfaces (and, more generally for higher-dimensional manifolds), that are embedded in a Euclidean space, the concept of curvature is more complex, as it depends on the choice of a direction on the surface or manifold. This leads to the concepts of maximal curvature, minimal curvature, and mean curvature.

For Riemannian manifolds (of dimension at least two) that are not necessarily embedded in a Euclidean space, one can define the curvature intrinsically, that is without referring to an external space. See Curvature of Riemannian manifolds for the definition, which is done in terms of lengths of curves traced on the manifold, and expressed, using linear algebra, by the Riemann curvature tensor.

Examples of use of curvature
1. "Its curvature may have had something to do with it being misidentified.
2. Taylor said she was born with scoliosis, an abnormal curvature of the spine, and has osteoporosis.
3. My spine had a double curvature, which meant it was bent into an ‘S‘ shape.
4. Many people have a slight sideways curvature in their spine, which is considered normal.
5. Orthokeratology, now becoming widely available in Britain, uses contact lenses worn at night to correct the curvature of the eye.