ABSTRACT
The invention of the telescope in 1608 led to new observations undermining the geocentric picture, and rekindling interest in an infinite universe. Some peo ple were uncomfortable with an infinite universe, but didn’t like Aristotle’s boundary either. What would lie beyond the boundary? In his 1854 Habilitationschrift, Riemann proposed the three-sphere as a model of the universe. Recall from Chapter 14 that the threesphere is the three-dimensional surface of a four-di mensional ball. It’s a finite universe, yet has no trou blesome boundary.
