Is the problem [Coiling Rope in a Box][1] decidable?  To be specific, is this decidable? 

> Given $L > 0$ and $r \in (0,\frac{1}{2})$,
both rational,
can a rope of length $L$ and radius $r$ 
fit into a unit-cube box?

See the earlier *MO* question linked above for the problem definition.

It seems one would have to represent all possible rope curves with a finite set
of parameters, and then use Tarski's quantifier elimination.  But perhaps there are other
routes to determining decidability.


  [1]: http://mathoverflow.net/questions/26525/coiling-rope-in-a-box