Date: Nov 13, 2012 6:23 PM
Author: Brad Cooper
Subject: Curvature in Cartesian Plane

I expect that this is true...

We have three points on a Cartesian x-y plane, and the circle that passes through these three points has a constant curvature of k.

If we have a doubly differentiable curve in the x-y plane that passes through these points, is there always some point on the curve which has curvature k?

I am finding it tough to prove this. Any help appreciated.