# Thread: True or false, limits curvature

1. ## True or false, limits curvature

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?

2. 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.

3. so the lim kr as r approaches infinity would = 0 not infinity, correct? so Its false still

4. That is correct.