Let a regular curve be defined as $\vec{\gamma}(t):I\to\mathbb{R}^n$. By regular, I mean that $\vec{\gamma}'(t)$ is never the zero vector. Is there an upper bound on its curvature? What is a good way of thinking about this? I really appreciate examples because I'm new to the topic.

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    $\begingroup$ No there isn't. Think of circles of smaller and smaller radius. The curvatures get larger and larger $\endgroup$ Sep 23 '20 at 7:40

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