True or False: Let Kr be the curvature of a circle of radius r (in R2) then lim as r approaches infinity Kr=1.
I say false because as r approaches infinity the Kr= infinity.
Is that right?
On a circle of radius $\displaystyle r$, the curvature is uniformly $\displaystyle \frac{1}{r}$.
We know this because the curvature on the unit circle is uniformly $\displaystyle 1$, and on an arc-length-paramatrized circle of radius $\displaystyle r$, $\displaystyle \mathbf{p'}(s)$ changes $\displaystyle 1/r$ as fast.