Optimal packings of two to four equal circles on any flat torus
M Brandt, W Dickinson, AV Ellsworth, J Kenkel… - Discrete …, 2019 - Elsevier
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.
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.
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.
Elsevier