 
Summary: Ruler and compass constructions.
1. Definition. Suppose S C. We let
l(S)
be the set of lines in C at least two points of which are in S. We let
c(S)
be the set of circles in C whose centers are in S and at least one point of which is in S. We let (S) be the
set of points z C such that z S or
z L1 L2 for two nonparallel lines L1 and L2 in l(S)
or
z L C for some line L l(S) and some circle C c(S)
or
z C1 C2 for two distinct circles C1 and C2 in c(S).
2. Definition. We set
K =
n=0
n
({0, 1});
A point of K is said to be constructible.
Our goal is to prove the
