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.
Read more about Surface.
Some articles on surface:
... The field's surface, originally composed of AstroTurf, contained many gaps and uneven patches ... Baseball players also complained about the surface ... It was much harder than other AstroTurf surfaces, and the shock of running on it often caused back pain ...
... a set of reference points on the Earth's surface against which position measurements are made and (often) an associated model of the shape of the Earth (ref ... used for describing a point on the Earth's surface, in latitude and longitude or another coordinate system ... In engineering and drafting, a datum is a reference point, surface, or axis on an object against which measurements are made ...
... In a hard drive, the heads 'fly' above the disk surface with clearance of as little as 3 nanometres ... is controlled by the design of an air-bearing etched onto the disk-facing surface of the slider ... height constant as the head moves over the surface of the disk ...
... the boundary of a cube, are among the first surfaces encountered in geometry ... It is also possible to define smooth surfaces, in which each point has a neighborhood diffeomorphic to some open set in E² ... This elaboration allows calculus to be applied to surfaces to prove many results ...
... The Roman surface or Steiner surface (so called because Jakob Steiner was in Rome when he thought of it) is a self-intersecting mapping of the real projective plane into three-dimens ... sphere in terms of longitude (θ) and latitude (φ), gives parametric equations for the Roman surface as follows x = r2 cos θ cos φ sin φ y = r2 sin θ cos φ sin φ z = r2 ... a triple point, and each of the xy-, yz-, and xz-planes are tangential to the surface there ...
More definitions of "surface":
- (noun): The outer boundary of an artifact or a material layer constituting or resembling such a boundary.
Example: "There is a special cleaner for these surfaces"; "the cloth had a pattern of red dots on a white surface"
- (verb): Appear or become visible; make a showing.
Example: "I hope the list key is going to surface again"
Synonyms: come on, come out, turn up, show up
- (adj): On the surface.
Example: "Surface materials of the moon"
- (noun): The outermost level of the land or sea.
Example: "Earthquakes originate far below the surface"; "three quarters of the Earth's surface is covered by water"
Synonyms: Earth's surface
- (verb): Put a coat on; cover the surface of; furnish with a surface.
- (noun): Information that has become public.
Example: "The facts had been brought to the surface"
- (noun): The extended two-dimensional outer boundary of a three-dimensional object.
Example: "They skimmed over the surface of the water"; "a brush small enough to clean every dental surface"; "the sun has no distinct surface"
- (noun): A superficial aspect as opposed to the real nature of something.
Example: "It was not what it appeared to be on the surface"
Famous quotes containing the word surface:
“A lifeless planet. And yet, yet still serving a useful purpose, I hope. Yes, a sun. Warming the surface of some other world. Giving light to those who may need it.”
—Franklin Coen, and Joseph Newman. Exeter (Jeff Morrow)
“All forms of beauty, like all possible phenomena, contain an element of the eternal and an element of the transitoryof the absolute and of the particular. Absolute and eternal beauty does not exist, or rather it is only an abstraction creamed from the general surface of different beauties. The particular element in each manifestation comes from the emotions: and just as we have our own particular emotions, so we have our own beauty.”
—Charles Baudelaire (18211867)
“A society which allows an abominable event to burgeon from its dungheap and grow on its surface is like a man who lets a fly crawl unheeded across his face or saliva dribble unstemmed from his moutheither epileptic or dead.”
—Jean Baudrillard (b. 1929)