Curvature is a measure of geometric inhomogeneity. For different geometric shapes, flatness has different meanings. Curvature of curves and surfaces in Euclidean space. Please refer to curvature tensor for general curvature. In dynamics, generally speaking, when an object moves at variable speed relative to another object, it will also produce curvature. This is about the distortion of time and space. Combined with the equivalence principle of general relativity, an object with variable speed motion can be regarded as being in a gravitational field, resulting in curvature.
Curvature of a curve is the rotation rate of the tangent direction angle of a point on the curve to the arc length, which is defined by differential and represents the degree to which the curve deviates from a straight line. A numerical value that mathematically represents the degree of curvature of a curve at a certain point. The greater the curvature, the greater the curvature of the curve. The reciprocal of curvature is the radius of curvature.
Brief introduction of curvature of parametric equation;
Parametric equation, as a mathematical term, is similar to a function: all numbers in a specified set, called parameters or independent variables, determine the result of the dependent variable. For example, kinematics, the parameter is usually "time", and the result of the equation is speed, position and so on.
Mbth is a quantity that describes the degree of geometric bending, such as the degree to which a surface deviates from a plane or the degree to which a curve deviates from a straight line. In different fields of geometry, the specific definition of curvature is not exactly the same.
Curvature can be divided into external curvature and internal curvature, and there are important differences between them. The former definition needs to embed geometry into Euclidean space, while the latter is directly defined on Riemannian manifold. Curvature is a measure of geometric inhomogeneity. For different geometric shapes, flatness has different meanings.