- #1

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when measuring length of geodesic shortest paths, or more in general, when measuring the length of a parametric curve in the space, what we usually do is to sum the length of infinitesimal arcs of that curve, assuming an

*euclidean norm*.

Why this choice?

I have not found in literature any mention on the possibility of using other norms, like L1-norm.

Why not to allow to measure the length of infinitesimal arcs of a curve in [tex]\mathbb{R}^2[/tex] by doing instead:

[tex]ds = \left| \frac{\partial \mathbf{p}}{\partial x} \right| dx + \left| \frac{\partial \mathbf{p}}{\partial y} \right| dy[/tex]

Thanks...