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properties of parallel curves

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 constant).

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.

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

The parallelism of curves is an equivalence relation.
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