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
Isosceles triangle formula_10. When the isoperimetric inequality becomes an equality, there is only one such triangle, which is equilateral. If the two equal sides have length formula_2 and the other side has length formula_3, then the internal angle bisector formula_22 from one of the two equal-angled vertices satisfies as well as and conversely, if the latter condition holds, an isosceles triangle parametrized by formula_2 and formula_22 exists. The Steiner–Lehmus theorem states that every triangle with two angle bisectors of equal lengths is isosceles. It was formulated in 1840 by C. L. Lehmus. Its other namesake, Jakob Steiner, was one of the first