The Modern Analysis of the Problem of Multisecting an Angle

Abstract

The work is devoted theoretical and practical analysis of an actual problem – the problem of multisecting (in particular, trisecting) an angle, i.e. the problem of division of a given arbitrary angle into the given set of equal parts using only a compasses and an unmarked straightedge. General statement of a problem is formulated. The mathematical analysis of the problem (within the framework of the theories of similarity of triangles and of similarity of concentric circles) and the logical analysis of the problem are proposed. It is proved that practical solution of the problem of multisecting an arbitrary angle with only a compasses and an unmarked straightedge is impossible because an arc cannot be transformed to the straight line segment with a compasses and a straightedge.