three body problem central configurations

All 99 (complex) solutions of the Albouy-Chenciner equations for central configurations of the Newtonian three-body problem, with equal masses. There are three "distances" for each solution; each set of distances are drawn as a triangle. The unit circle is included for a sense of scale. The solutions of primary interest are real, but understanding the complex solutions is important for analyzing these equations.

This was computed with Sage, with the bulk of the work was done with Jan Verschelde's PHCpack. At the moment, PHCpack is in sage as an optional package, so you would have to install that to get the code to work: source code.