Regularity of curves with a continous tangent line

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This note contains a proof of the fact that a Jordan curve in ℝ2 with a continuous tangent line at each point admits a regular reparameterization. We extend the result both to more general curves in ℝn and to higher orders of differentiability. © 2009 Australian Mathematical Society.
Original languageEnglish
Pages (from-to)17-26
JournalJournal of the Australian Mathematical Society
Issue number1
Publication statusPublished - 1 Feb 2009


  • Jordan curve
  • Order of differentiability
  • Regular curve
  • Tangent line


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