# Is there an upper bound for the curvature of a regular curve?

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.

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