In mathematics, specifically in topology, a surface is a two-dimensional manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space, E³. On the other hand, there are also more exotic surfaces, that are so "contorted" that they can't be embedded in three-dimensional space at all. To say that a surface is "two-dimensional" means that, about each point, there's a coordinate patch on which a two-dimensional coor… (More on Surface)