Student Summer Scholars


High Density Packing, Equal Circles, Triangle Flat Torus


Geometry and Topology




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.