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 near-cancellation between the semiperimeter and side length in those triangles. If the apex angle formula_7 and leg lengths formula_8 of an isosceles triangle are known, then the area of that triangle is: This is a special case of the general formula for the area of a triangle as half the product of two sides times the sine of the included angle. The perimeter formula_10 of an isosceles triangle with equal sides formula_2 and base formula_3 is just As in any triangle, the area formula_5 and perimeter formula_10 are related by the isoperimetric inequality This is a strict inequality for isosceles