define what is curvature
Answers
Explanation:
In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object such as a surface deviates from being a flat plane, or a curve from being straight as in the case of a line,but this is defined in different ways depending on the context. There is a key distinction between extrinsic curvature, which is defined for objects embedded in another space(usually a Euclidean space)- in a way that touch the object, and intrinsic curvature,which is defined at each point in a Riemannian manifold.
The canonical example of extrinsic curvature is that of a circle, Which has a curvature equal to the reciprocal of it's radius everywhere. Smaller circles bend more sharply, and hence have higher curvature. The curvature of a smooth curve is defined as the curvature of it's osculating circle at each point.
The mathematical notion of curvature is also defined in much more general contexts. Many of these curvature as it is understood in lower dimensions.
The curvature of a curve naturally be considered as a kinematic quantity
The curvature depends on how nearby test particles diverge or converge when they are allowed to move freely in the space