So the key here is that cos(pi/5) = phi/2. From there, you could relate pi and phi in many ways. The proof of cos(pi/5) is quite simple, neatly done here: http:

So the key here is that cos(pi/5) = phi/2. From there, you could relate pi and phi in many ways. The proof of cos(pi/5) is quite simple, neatly done here: http://faculty.wwu.edu/curgus/Courses/125/Pentagon.pdf http://faculty.wwu.edu/curgus/Courses/125/Pentagon.pdf