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Using a rusty compass (a compass whose distance between the two needles can't be altered) divide a given line segment ${AB}$ into $n$ equal parts. In fact, a straightedge isn't provided.

I know that whenever a compass-and-straightedge construction can be done, a compass-only construction is possible.

Mathejunior
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    Is the width of the compass an a priori of the problem, or can it be chosen arbitrarily, as long as it is chosen once and for all? Because if the width of the compass happens to be the length of the segment (say, $=1$), the set of constructible points should just be the lattice of $\Bbb Z+\Bbb Z\frac{1+i\sqrt3}2$ which does not contain points of $\Bbb Q\setminus\Bbb Z$ at all. –  Sep 09 '17 at 06:48
  • @G.Sassatelli All that's provided is: the length of compass is pre-provided and $AB$ is a given segment as well. – Mathejunior Sep 09 '17 at 06:51

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