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.
Famous quotes containing the word surface:
“Weve forgotten what its like not to be able to reach the light switch. Weve forgotten a lot of the monsters that seemed to live in our room at night. Nevertheless, those memories are still there, somewhere inside us, and can sometimes be brought to the surface by events, sights, sounds, or smells. Children, though, can never have grown-up feelings until theyve been allowed to do the growing.”
—Fred Rogers (20th century)
“Here Men from The Planet Earth
First Set Foot upon The Moon
July, 1969 AD
We Came in Peace for All Mankind”
—Plaque left behind on the moons surface by the crew of Apollo 11.
Shaking the heavy dews from bloom and frond.
Bursting the surface of the ebony pond.”
—Wilfred Owen (18931918)