Angle trisection with coefficients in the field generated by these numbers. Therefore, any number that is constructible by a sequence of steps is a root of a minimal polynomial whose degree is a power of two. Note also that radians (60 degrees, written 60°) is constructible. The argument below shows that it is impossible to construct a 20° angle. This implies that a 60° angle cannot be trisected, and thus that an arbitrary angle cannot be trisected. Denote the set of rational numbers by . If 60° could be trisected, the degree of a minimal polynomial of over would be a power
Schwarz triangle function a vertex of the polygon "P" makes an angle of less than 2/3 with each of the edges of the polygon at that vertex if exactly two triangles of "P" meet at the vertex, since each has an angle less than or equal to /3 at that vertex. To check this is true when three triangles of "P" meet at the vertex, "C" say, suppose that the middle triangle has its base on a side "AB" of "P". By induction the radii "OA" and "OB" makes angles of less than or equal to 2/3 with the edge "AB". In this