ABSTRACT

The first three axioms are the Thalian constructions which ensure that we have a field after we have a nonreal complex number z. Some properties of these constructions include the following: reflections can be folded; the set of slopes of fold lines correspond to the points constructed on the imaginary axis together with oo; the points which can be constructed contain the field Q(z) and is contained in Q(z,i); and starting with z = 1+^v3, the point i cannot be constructed.