Still the curvature (I)
Imagine a car, moving at constant speed 1, that describes the following path:
The car initially moves straight; then turn left and turn right and then backs to move in a straight line. Then:
|sign of curvature||0||+||-||0|
Therefore, the curvature is given by a graph of the following type:
To find out if you can identify the curvature function of a given curve, play the following games:
In fact, any smooth curve has its curvature function. To construct it, assume a particle ("our car") is describing the curve with constant speed 1 and observe how the curve changes with respect to its successive tangent lines.