Having a little trouble with part b.
Is there a way to show that this curve would be arc length paramaterized? I am assuming that we cannot say this.
If it is not we can take alpha', alpha'' and then compute curvature through
|alpha' x alpha"|/ |alpha'|^3
This is the brute force method to solve this problem, which is very messy. However, I am assuming that there is another way to solve this problem, but I seem to be missing a theorem that could push me in the right direction. Any hints? Thank you!
2026-03-28 21:06:31.1774731991
Curvature proof of a convex plane curve
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Hmm, you shouldn't be posting my textbook on here without permission. (You seem to be pasting in a number of exercises from it. Please stop.) Although you can use the formula you cited, you can also just use the usual chain rule computation to adjust for non-arclength-parametrized curves. The crucial thing to think about is what the unit tangent vector $\mathbf T(\theta)$ is.