Constructing π from a regular star-12-gon

Of course, just approximately! It is not possible to create the exact length π from the unit length by using a compass and a straightedge, since π is a transcendental number, and only (certain) algebraic numbers can be constructed in that way. In this figure all sides of the regular star-12-gon are 1 unit long. By following the figure (that is, R is the intersection of AB and CD, and S is the intersection of EF and GH), the length of RS is very close to π, its accuracy is 4 digits. In fact, the length of RS is the same as the one can be obtained by using Kochański's construction (1685). This construction was found by the RegularNGons program with the input n=12, case 43261.