  The Dedekind tessellation -- the regular tessellation of the upper half-plane
by the Mobius action of the modular group -- is usually viewed as a system of
ideal triangles. We change the focus from triangles to circles and give their
complete algebraic characterization with the help of a representation of the
modular group acting by Lorentz transformations on Minkowski space. This
interesting example of the interplay of geometry, group theory and number
theory leads also to convenient algorithms for computer drawing of the Dedekind
tessellation.
