Abstract

The paper is devoted to exposition of constructions with straightedge and compass, constructible numbers and their position with respect to all algebraic numbers. Although the large number of constructions may be accomplished with straightedge and compass, one of the known problems of this kind dating from Greek era is duplication of a cube. The given proof in this paper is elementary and self-contained. It is suitable for teachers, as well as for high school students.

Keywords: Duplication of a cube; construction with compass and straightedge; constructible number; algebraic number.

Pages:  51$-$61     

Volume  XIII ,  Issue  1 ,  2010