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 differentiation and represents the degree of deviation of the curve 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.
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 differentiation and represents the degree of deviation of the curve 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.
Curvature is a measure of geometric inhomogeneity. For different geometric shapes, flatness has different meanings.
In this paper, we consider the 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.
According to the explanation of general relativity, in the gravitational field, the nature of space-time is determined by the "mass" distribution of objects, which makes the nature of space-time uneven and causes the curvature of space-time. Because objects with mass will bend space-time, and you can think that with speed, objects with mass will become heavier and the curvature of space-time will be greater.
In physics, curvature is usually obtained by normal acceleration (centripetal acceleration). See normal acceleration for details.