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Non-existence of rational arc length parameterizations for curves in \(\mathbb R^n\). (English) Zbl 1166.53002

Summary: We show, as a generalization of prior results for \(\mathbb R^2\) and \(\mathbb R^3\), that for all \(n\geq 2\) the only curves in \(\mathbb R^n\) with rational arc length parameterizations are straight lines.

MSC:

53A04 Curves in Euclidean and related spaces
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