Try the following experiment. Get a tangerine and attempt to take the peel off in one piece. Lay the peel flat and see what you notice about the shape. Repeat several times. This can be done with many types of citrus fruit. Clementines work especially well.

Cornell mathematics professor William P. Thurston used this experiment to help students understand the geometry of surfaces. Thurston, who won the Fields Medal in 1982, was well known for his geometric insight. In the early 1980s, he made a conjecture, called the*geometrization conjecture,*about the possible geometries for three-dimensional manifolds. Informally, an n-dimensional