In the previous post, I introduced to you the 0.0001 Time Rate approach This post is an extended application of the said technique on curvatures and radius of curvatures.

**Curvature** is defined (*by The Facts on File Dictionary of Mathematics*) as the rate of change of the slope of the tangent to a curve. For each point on a smooth curve there is a circle that has the same tangent and the same curvature at that point. The radius of this circle called the “**radius of curvature**”, is the reciprocal of the curvature, and its center is known as the center of curvature. If the graph of a function y=f(x) is a continuous curve, the slope of the tangent at any point is given by the derivative dy/dx and the curvature is given by

and the radius of curvature is given by

where: is the derivative of with respect to and is the second derivative of y with respect to x or in simpler terms, it is the derivative of . Continue reading