/sci/ - Science & Math

>>11513419
Right, I get you.
Maybe we just interpreted the circle counter-example incorrectly. It's constant, so the arc parametrization is just [math]\{ 0 \] \rightarrow \mathbb{R}^2 [/math], and since the derivative doesn't exist (by definition), it's not zero, so it's regular in an extremely degenerate sense.
So you've got three cases:
>[math]k'[/math] zeroes in an open set means it degenerates in a regular way
>k' doesn't zero is done
>k' zeroes in one point or in [a, b] are still up for the corners