English

Length of parallel curves

Differential Geometry 2007-11-13 v1

Abstract

We prove that the length difference between a closed periodic curve and its parallel curve at a sufficiently small distance is proportional to the rotation index. As an application, the rotation index of a curve could be estimated by means of Cauchy-Crofton formula.

Keywords

Cite

@article{arxiv.0711.1670,
  title  = {Length of parallel curves},
  author = {Enrique Macias Virgós},
  journal= {arXiv preprint arXiv:0711.1670},
  year   = {2007}
}

Comments

5 pages, 2 figures

R2 v1 2026-06-21T09:42:19.241Z