Title: Optimal Packings of Two to Four Equal Circles on Any Flat Torus,
Abstract: We find explicit formulas for the radii and locations of the circles in all
the optimally dense packings of two, three or four equal circles on any flat
torus, defined to be the quotient of the Euclidean plane by the lattice
generated by two independent vectors. We prove the optimality of the
arrangements using techniques from rigidity theory and topological graph
theory.