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A surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero. This is analogous to a curve generalizing a straight line

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Another type of derivative, and the associated primitive

Let $\mathbf{v}:(a,b)\to\mathbb{R}^2$ be a continuous function, such that $||\mathbf{v}(t)||=1,\ \forall t\in (a,b)$. Find all continuous functions $\mathbf{r}:(a,b)\to\mathbb{R}^2$ so that: $ \mathb …