properties of parallel curves

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Two plane curves are parallel curves of each other, if every normal of one curve is also a normal of the other curve (then one may show that the distance of the corresponding points of the curves is a ).

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Two curves are parallel curves of each other, if they are the loci of the end points^{} of a line segment^{} which moves perpendicularly to its own direction.

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Every regular curve having a continuous^{} curvature has an infinite^{} family of parallel curves.

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The parallelism^{} of curves is an equivalence relation^{}.

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The two parallel curves ${\gamma}_{\pm a}$ on both sides of a curve $\gamma $ at the distance $a$ form the envelope of the family of circles with center on $\gamma $ and radius $a$.
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Title  properties of parallel curves 

Canonical name  PropertiesOfParallelCurves 
Date of creation  20130322 17:14:30 
Last modified on  20130322 17:14:30 
Owner  pahio (2872) 
Last modified by  pahio (2872) 
Numerical id  6 
Author  pahio (2872) 
Entry type  Topic 
Classification  msc 51N05 