﻿ Definition of curvature - What it is, Meaning and Concept - I want to know everything - 2021

# Curvature

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The Latin word curvature came to our language as curvature . The concept refers to the curved condition (hunched over or crooked). The idea of ​​curvature is also used with respect to deviation which has a curved line with respect to a line. For example: "The criminals tried to take advantage of the curvature of the wall to hide, but were discovered", “Bad body posture can cause, in the long term, the curvature of the column vertebral ”, “The curvature of the screen surprised the public”.

If someone talks about the curvature of a television, to name a case, it refers to the fact that its screen is not straight. The curvature of a phone Cellular (mobile), meanwhile, is linked to its curved edges. In these cases, the curvature can represent both an aesthetic and functional aspect, or a fusion of both. Regardless of the purpose of this feature in an appliance, electronic device or car, among other products, fashion trends make it inevitable that their duration is limited, so that sooner or later the curvature is replaced by angled edges, and vice versa.

In the field of geometry and mathematics, the curvature can be the magnitude or the number which measures this quality. It is, in this framework, that quantity that a geometric object deviates from a line or a plane.

The notion of spacetime curvature derives from the general relativity theory , which postulates that the gravity It is an effect of the curved geometry that spacetime has. According to this theory, the bodies that are in a gravitational field make a curved path in space. The curvature of spacetime is measured according to the call curvature tensioner or Riemann tensioner .

He curvature displacement , on the other hand, is a theory which indicates that a vehicle could travel at a speed greater than the speed of light from a distortion that generates greater curvature in space-time.

There is a magnitude called Radius of curvature which is used to measure the curvature of an object belonging to geometry as if it were a surface, a curved line or, more generally, a differentiable variety which is in a euclidean space.

If we take as reference an object or a curved line, its radio of curvature is a geometric magnitude that we can define in each of its points, and is equivalent to the inverse of the absolute value of the curvature in all of them. We must not forget that the curvature is the alteration that crosses the direction of the tangent vector to a given curve as we move along it.

One of the measurements that we can perform on a given surface is the gaussian curvature , a number belonging to the set of reals that represents the intrinsic curvature for each of the regular points. It is possible to calculate it based on the determinants of the two fundamental forms of the surface.

The first fundamental form of the surface is a 2-covariant tensor that presents symmetry and defined in the tangent space to each of the points of the same; it is the metric tensor (that is, range 2, used for the definition of concepts such as volume, angle and distance) that induces the Euclidean metric on the surface. The second, on the other hand, is the projection of the covariant derivative that is carried out on the surface-normal vector, and is induced by the first fundamental form.

In general, the Gaussian curvature is different at each point of the surface and is related to its main curvatures. The sphere It is a special case of surface, since in all its points it has the same curvature.

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