Non-existence of rational arc length parameterizations for curves in Rn
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摘要
We show, as a generalization of prior results for R2 and R3, that for all n≥2 the only curves in Rn with rational arc length parameterizations are straight lines.
论文关键词：Arc length,Rational curves,Natural parameterization,Pythagorean equation,Integration of rational functions,Residues
论文评审过程：Received 7 May 2008, Revised 15 August 2008, Available online 27 September 2008.
论文官网地址：https://doi.org/10.1016/j.cam.2008.09.022
