We have defined the curvature as the slope of the slope,
d(dy/dx)/dx =
d2y/dx2,
in order to give an "obvious" meaning to the second derivative.
Although this definition is simple, intuitive and useful,
it is not the
conventional mathematical definitiond/ds,
where is the tangential angle
and s is the arc length.
(So shoot me. I still like mine better.
;-)
Thanks to Mitchell Timin for pointing this out.
- A SKEPTICs GUIDE 
d
/ds,
where