curvature

The first idea of curvature(Fig.1) is that

when you walk 1 meter,  how much you fall or rise.

In this idea, the curvature of a line is zero.

In Fig.1 [A] and [B], we can understand that

the longer the radius of a circle is, the shorter the distance of fall is.

When the radius is shorter than 1 meter, we cannot define curvature(Fig.1 [C]).

The second idea of curvature(Fig.2) is that

when you walk from the point P to the point Q (meaning the distance, Δs),

we could value at the angle between the two vectors a and b for Δs,

where the vector a is the tangent at the point P and the vector b is the tangent at the point Q.