Surface

In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.

To say that a surface is "two-dimensional" means that, about each point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the Earth is (ideally) a two-dimensional sphere, and latitude and longitude provide two-dimensional coordinates on it (except at the poles and along the 180th meridian).

The concept of surface finds application in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface.

Read more about Surface:  Definitions and First Examples, Extrinsically Defined Surfaces and Embeddings, Construction From Polygons, Connected Sums, Closed Surfaces, Surfaces in Geometry

Other articles related to "surface, surfaces":

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Roman Surface
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Veterans Stadium - Playing Surface
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Famous quotes containing the word surface:

    But the surface of the Earth was meant for man. He wasn’t meant to live in a hole in the ground.
    Edward L. Bernds (b. 1911)

    The surface of the ground in the Maine woods is everywhere spongy and saturated with moisture.
    Henry David Thoreau (1817–1862)