Curves
and Surfaces > Surfaces
Maps from R^{2} into R^{3}. |
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Intuitively, when we think of surfaces, we might think of ripples on the surface of a pond, a tabletop, or the outside covering of a globe. In a mathematical sense, most surfaces are like a plane bent smoothly in space (possibly with self-intersections, singularities, and other oddities.) That is, they are subsets of R^{3} that are in some sense 2-dimensional. More precisely, a surface is defined by a map from R^{2} into R^{3}. |