  The universe displays a three-dimensional pattern of hot and cold spots in
the radiation remnant from the big bang. The global geometry of the universe
can be revealed in the spatial distribution of these spots. In a topologically
compact universe, distinctive patterns are especially prominent in spatial
correlations of the radiation temperature. Whereas these patterns are usually
washed out in statistical averages, we propose a scheme which uses the
universe's spots to observe global geometry in a manner analogous to the use of
multiple images of a gravitationally lensed quasar to study the geometry of the
lens. To demonstrate how the geometry of space forms patterns in observations
of the microwave sky, we develop a simple real-space approximation to estimate
temperature correlations for any set of cosmological parameters and any global
geometry. We present correlated spheres which clearly show geometric pattern
formation for compact flat universes as well as for the compact negatively
curved space introduced by Weeks and another discovered by Best. These examples
illustrate how future satellite-based observations of the microwave background
can determine the full geometry of the universe.
