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

Takis Sakkalis; Rida T. Farouki; Leonid Vaserstein

doi:10.1016/j.cam.2008.09.022

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

Takis Sakkalis, Rida T. Farouki, Leonid Vaserstein

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	494-497
Number of pages	4
Journal	Journal of Computational and Applied Mathematics
Volume	228
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2008.09.022
State	Published - Jun 1 2009

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2008.09.022

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title = "Non-existence of rational arc length parameterizations for curves in Rn",

abstract = "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.",

author = "Takis Sakkalis and Farouki, {Rida T.} and Leonid Vaserstein",

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AU - Sakkalis, Takis

AU - Farouki, Rida T.

AU - Vaserstein, Leonid

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Y1 - 2009/6/1

N2 - 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.

AB - 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.

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M3 - Article

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

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

Abstract

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