> Can you put an "real helix" beside my "false helix"

I've attached here a helix created from Rhino - I think it is approximated to a true helix within 0.01 units. (A NURBS curve cannot actually have a 100% exact shape of a helix unlike a circle, it has to be approximated to some tolerance).

Your curve is very, very close - your curve has a maximum deviation of 0.04 units from this one.

- Michael