Non-existence of rational arc length parameterizations for curves in Rn

Authors:
Takis Sakkalis;Rida T. Farouki;Leonid Vaserstein
Affiliations:
Mathematics Laboratory, Agricultural University of Athens, 75 Iera Odos, Athens 11855, Greece;Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA 95616, USA;Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

We show, as a generalization of prior results for R^2 and R^3, that for all n=2 the only curves in R^n with rational arc length parameterizations are straight lines.