Manuel Hemström: Field Extensions and Straightedge and Compass Constructions

Abstract.

This bachelor thesis explores the use of Field Extensions on Straightedge and Compass Constructions in order to refute the Three Classical Problems: (1) Doubling the Cube, (2) Trisecting the Angle, (3) Squaring the Circle. By applying the theory of Field Extensions, we demonstrate that these age-old conjectures are inherently unsolvable within the framework of constructible numbers.