I just came across a page on Interactive Mathematics. The motto of this site is „to learn math by playing with it“. It also features ads for Brasil stocks, and the 23 year old Yan He and some other beautiful girls of the same age – with pictures. Enjoy along with the Math Tutor DVD you can buy on this site.

What it does not provide is explanations. Or is it obvious why

\(\dfrac{(1+(dy/dx)^2)^{3/2}}{d^2y/dx^2} \)

is the radius of curvature? And what is an approximating circle, and why is one circle better than another? Admittedly the provided web apps are nice to play with.

In fact, it is not easy to prove hard facts about the curvature. However, on this Euler page, you find at least a motivation.