Is there some simple description of which complex numbers are "constructible" with straightedge and compass and neusis?


See <http://en.wikipedia.org/wiki/Constructible_number> and <http://en.wikipedia.org/wiki/Neusis>.



Neusis constructions
Just as straightedge and compass constructions give the numbers in the closure
of the rationals under square roots, neusis gives the closure of the rationals
under square roots *and* cube roots.


For more details, also for an alternate characterization in terms of
origami, see [this paper](http://www.math.sjsu.edu/~alperin/TRFin.pdf) by Roger Alperin.


