High Density Packing, Equal Circles, Triangle Flat Torus
Geometry and Topology
Castelaz, Anna; Dickinson, William; Guillot, Daniel; and Xhumari, Sandi, "Optimal Packings of up to 6 Equal Circles on a Triangular Flat Torus" (2008). Student Summer Scholars. 12.
How do you optimally pack equal circles into the standard triangular torus? In this paper, we proved the optimal packings of 1 through 6 equal circles. In order to do this we used techniques from graph theory and also mathematical softwares like Maple and LaTeX. I only worked on proving the optimal packing of 6 equal circles on this special container called the standard triangular torus. In addition, I also contributed in improving the previous proofs for 5 or less equal circles. The purpose of my research was to prove the best packing of 6 equal circles into this at tori and I achieved it.