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
Sierpinski triangle converge on the Sierpinski triangle. This is what is happening with the triangle above, but any other set would suffice. If one takes a point and applies each of the transformations "d", "d", and "d" to it randomly, the resulting points will be dense in the Sierpinski triangle, so the following algorithm will again generate arbitrarily close approximations to it: Start by labeling p, p and p as the corners of the Sierpinski triangle, and a random point v. Set , where "r" is a random number 1, 2 or 3. Draw the points v to v. If the first