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``Re: Catenary'' by rspuzio on 2007-07-09 18:38:32
> I am not sure, but the implicit equation seems of a smooth curve
> while the parallel curve is not.

This is actually a common phenomenon,

> Perhaps it has this something to do with the multi-valued
> functions involved?

It has to do wit curvature --- when the distance to the curve
equals the radius of curvature, one can expect a singularity
at that point.
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