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Summary: Ruler and compass constructions.
1. De nition. 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 2 C such that z 2 S or
z 2 L 1 \ L 2 for two nonparallel lines L 1 and L 2 in l(S)
or
z 2 L \ C for some line L 2 l(S) and some circle C 2 c(S)
or
z 2 C 1 \ C 2 for two distinct circles C 1 and C 2 in c(S):
2. De nition. We set
K =
1
[
n=0
n (f0; 1g);
A point of K is said to be constructible.
Our goal is to prove the
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