surface, Ingeometry, a two-dimensional collection of points (flat surface), a three-dimensional collection of points whosecross section is acurve (curved surface), or the boundary of any three-dimensional solid. In general, a surface is acontinuous boundary dividing a three-dimensional space into two regions. For example, the surface of asphere separates the interior from the exterior; a horizontal plane separates the half-plane above it from the half-plane below. Surfaces are often called by the names of the regions they enclose, but a surface is essentially two-dimensional and has an area, while the region it encloses is three-dimensional and has a volume. The attributes of surfaces, and in particular the idea ofcurvature, are investigated indifferential geometry.