Constructions with ruler and compass and galois Theory

Specialeforsvar ved Konstantinos Mitsainas

Titel: Constructions with ruler and compass and Galois Theory

Resume:  This Master's thesis is about constructions with straightedge and compass, analyzed via Galois theory. The goal is to see how we can use Galois theory in order to understand various constructions, mainly the construction of the regular 17-gon. We will see the procedure Gauss used in order to prove the constructibility of the regular 17-gon, using so-called periods, after having discussed more basic constructions. After that we present a simpler proof of the constructibility of the 17-gon, as well as the geometrical construction of it by Richmond. Finally we report on how the theory that we use for the construction of the regular 17-gon can be extended to the problem of division of the arc of the lemniscate. 

Vejleder:  Ian Kiming
Censor:    Tom Høholdt, DTU