has been replaced with SynergeticsAppTen.nb (540 KB) - Mathematica Version 7.0 1.0 Notebook.
The last graphic in the Notebook is followed by a question about the speed of the convergence of a general root finding method. The guesses for the third iteration on, could be found with the vector equation method shown in the section "Solving Matrix Problems Using Bucky Numbers" or trigonometry.
I don't think Newton's method can be beat, I've tried and tried, but if anyone could beat Newton it would be Bucky Fuller. How does the speed of convergence compare for polynomials in general? What is the traditional name for this kind of root finding method? Has it been done with the Cartesian coordinate system?