정n각형의 작도 가능성에 관한 연구

Abstract

This research aims to explore the 3 geometric construction problem and the problem of constructibility of regular -sided polygons using the theories of abstract algebra such as field theory and Galois theory. Additionally, the significance and benefits of these findings for mathematics education were considered. In the introductory, the importance of connections in mathematics, such as the connection between geometry and algebra was highlighted as the background of the research. Firstly, we study the extension field and the Galois theory as background, then examine the straightedge and compass construction and constructible numbers. And based on the above contents, the proof of the 3 geometric construction problem and the problem of constructibility of regular -sided polygons was introduced. Finally, in the discussion, the significance and benefits that Euclidean construction can give to mathematics education and the importance of connection between the domains of mathematics in mathematics education were considered.