The curvature k of a circle is equal to the reciprocal of the radius of the circle, that is, k =1/r.

The derivation process is (where △a is the change degree of the central angle, expressed as △s/R in radians).

△a/△s

=△s/R/△s

= 1/R

Curvature 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 the 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.

Extended data:

The meaning of curvature:

Curvature is a measure of geometric inhomogeneity. For different geometric shapes, flatness has different meanings.

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.