Length of parallel curves

2007/11/11 by Enrique Macias Virgós, Virgós, Enrique Macias
Engineering · Mathematics · #53A04 #53C65 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities #math.DG #msc:53A04 #msc:53C65

paper · pdf · doi:10.48550/arxiv.0711.1670

5 pages, 2 figures

arxiv created 2007/11/11 · openalex publication_date 2007/11/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

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.

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