Computer Graphics Tools for Rendering Algebraic Surfaces and for Geometry of Order

New developments in interactive computer graphics make it possible for mathematicians to approach old subjects in fresh ways. Occasionally the new approaches reveal additional insights into things already well understood from other viewpoints. This note give several examples of projects developed in collaboration with undergraduate students at Brown University in courses related to differential geometry. In each case, computer graphics techniques are used to investigate some geometric phenomenon, and in each case the difficulties encountered by the program reveal some feature of geometric interest.