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*<math>k_d(t)=\frac{k(t)}{1+dk(t)},\quad</math> with <math>k(t)</math> the [[curvature]] of the given curve and <math>k_d(t)</math> the curvature of the parallel curve for parameter <math>t</math>.
*<math>R_d(t)=R(t) + d,\quad</math> with <math>R(t)</math> the [[curvature#Curvature of plane curves|radius of curvature]] of the given curve and <math>R_d(t)</math> the radius of curvature of the parallel curve for parameter <math>t</math>.
* When they exist, the [[Osculating circle|osculating circles]] to parallel curves at corresponding points are concentric. <ref>Fiona O'Neill: [https://fionasmathblog.com/2022/04/26/planar-bertrand-curves-with-pictures/ ''Planar Bertrand Curves (with Pictures!).''] {{Webarchive|url=https://web.archive.org/web/20221011143632/https://fionasmathblog.com/2022/04/26/planar-bertrand-curves-with-pictures/ |date=2022-10-11 }}</ref>
*As for [[parallel (geometry)|parallel lines]], a normal line to a curve is also normal to its parallels.
*When parallel curves are constructed they will have [[Cusp (singularity)|cusp]]s when the distance from the curve matches the radius of [[curvature]]. These are the points where the curve touches the [[evolute]].
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*[http://xahlee.org/SpecialPlaneCurves_dir/Parallel_dir/parallel.html Visual Dictionary of Plane Curves] Xah Lee
* http://library.imageworks.com/pdfs/imageworks-library-offset-curve-deformation-from-Skeletal-Anima.pdf application to animation; patented as {{US patent|8400455}}
* http://www2.uah.es/fsegundo/Otros/Offset/16-SanSegundoSendraSendra-1532.pdf{{Dead link|date=August 2025 |bot=InternetArchiveBot |fix-attempted=yes }}
{{Differential transforms of plane curves}}
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