  We discuss methods for calculating Chern numbers of two-dimensional lattice
systems using spiral boundary conditions, which sweep all lattice sites in
one-dimensional order. Specifically, we establish the one-dimensional
representation of Fukui-Hatsugai-Suzuki's method, based on lattice gauge
theory, and the Coh-Vanderbilt's method, which relates to electronic
polarization. The essential point of this discussion is that the insertion of
flux into the extended one-dimensional chain generates an effective current in
the perpendicular direction. These methods are valuable not only for a unified
understanding of topological physics in different dimensions but also for
numerical calculations, including the density matrix renormalization group.
