Sakkalis, Takis; Farouki, Rida T.; Vaserstein, Leonid Non-existence of rational arc length parameterizations for curves in \(\mathbb R^n\). (English) Zbl 1166.53002 J. Comput. Appl. Math. 228, No. 1, 494-497 (2009). 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. Cited in 4 Documents MSC: 53A04 Curves in Euclidean and related spaces Keywords:arc length; rational curves; natural parameterization; Pythagorean equation; integration of rational functions; residues PDFBibTeX XMLCite \textit{T. Sakkalis} et al., J. Comput. Appl. Math. 228, No. 1, 494--497 (2009; Zbl 1166.53002) Full Text: DOI References: [1] Farouki, R. T., Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, (Geometry and Computing, vol. 1 (2008), Springer: Springer Berlin) · Zbl 1144.51004 [2] Farouki, R. T.; Sakkalis, T., Real rational curves are not unit speed, Comput. Aided Geom. Design, 8, 151-157 (1991) · Zbl 0746.41019 [3] Farouki, R. T.; Sakkalis, T., Rational space curves are not unit speed, Comput. Aided Geom. Design, 24, 238-240 (2007) · Zbl 1171.65331 [4] Henrici, P., Applied and Computational Complex Analysis, Vol. 1 (1974), Wiley: Wiley New York · Zbl 0313.30001 [5] Jacobson, N., Basic Algebra I (1985), W. H. Freeman & Co: W. H. Freeman & Co New York · Zbl 0557.16001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.