From the perspective of continuous differential geometry, this definition is also understandable, because curvature can be understood from the perspective of holography. There is nothing wrong with this topic as a middle school math problem. Although the background comes from differential geometry, apart from the background, the knowledge involved is completely elementary combinatorial mathematics.

You can know how much work has been done. Because the greater the radius of curvature, the more labor is saved, the greater the stress on the curve and the greater the distance traveled, so knowing these two parameters, we can calculate how much work has been done.

Curvature of plane curve:

For a plane curve C, the curvature of p at a point is equal to the reciprocal of the radius of an osculating circle, which is a vector pointing to the center of the circle. Its size can be measured by diopter, and 1 diopter is equal to every meter 1 (radian). The radius of this osculating circle is the radius of curvature.

The smaller the radius of the osculating circle, the greater the curvature; So when the curve is close to a straight line, the curvature is close to zero, and when the curve turns sharply, the curvature is very large.

The curvature of a straight line is 0 everywhere; The curvature of a circle with radius r is 1/r everywhere.