Durmus Samed Göker: Geometriska konstruktioner med linjal och passare - från geometri till algebra

Abstract: This thesis studies classical geometric constructions performed using only a straightedge and compass, with focus on both possible and impossible constructions. The work is grounded in the tradition of Euclidean geometry and begins by presenting theoretical framework and notation underlying constructible objects, accompanied by examples of constructions that can be carried within these constraints. The second part of the thesis addresses constructions that have been proven impossible, with particular emphasis on three classical problems: the squaring of the circle, the trisection of an angle, and the doubling of the cube. Using tools from modern algebra, especially the theory of field extensions, the thesis explains why these constructions cannot be achieved using classical geometric methods. By combining geometric intuition with algebraic theory, the thesis aims to clarify the distinction between possible and impossible constructions and to demonstrate how algebra provides rigorous criteria for constructibility