Considerable insight into elementary atomic theory is generated by constraining the atomic Hamiltonian of atoms with few electrons by demanding that the electrons be as far apart as possible. This and other simplifying assumptions allow us to separate Schrödinger's equation by reducing the problem to a geometrical analog. The analogous problem is to locate dots symmetrically on the surfaces of concentric spheres consistently with the Pauli principle and with the dots as far apart as possible. The resulting equations permit calculation of effective nuclear charges which are used to find the total energy of the system from a hydrogenlike energy formula. The energies so determined are compared to experimental values, and derived screening terms are compared to those of Slater's rules. Our energies are consistently lower than experimental values. Several unanswered questions opened by this technique are proposed as possible further research on a level suitable for an undergraduate paper.