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:
... Polyhedra, such as 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 ... allows calculus to be applied to surfaces to prove many results ...
... In surveying and geodesy, a datum is 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 (reference ellipsoid) to ... Horizontal datums are used for describing a point on the Earth's surface, in latitude and longitude or another coordinate system ... and drafting, a datum is a reference point, surface, or axis on an object against which measurements are made ...
... 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 ... 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 cos θ sin θ cos2 φ ... The origin is a triple point, and each of the xy-, yz-, and xz-planes are tangential to the surface there ...
... 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 ...
... In a hard drive, the heads 'fly' above the disk surface with clearance of as little as 3 nanometres ... the head is controlled by the design of an air-bearing etched onto the disk-facing surface of the slider ... the flying height constant as the head moves over the surface of the disk ...
More definitions of "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
- (verb): Put a coat on; cover the surface of; furnish with a surface.
- (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
- (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): 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"
- (noun): A superficial aspect as opposed to the real nature of something.
Example: "It was not what it appeared to be on the surface"
- (noun): A device that provides reactive force when in motion relative to the surrounding air; can lift or control a plane in flight.
Synonyms: airfoil, aerofoil, control surface
- (adj): On the surface.
Example: "Surface materials of the moon"
Famous quotes containing the word surface:
“If the man who paints only the tree, or flower, or other surface he sees before him were an artist, the king of artists would be the photographer. It is for the artist to do something beyond this: in portrait painting to put on canvas something more than the face the model wears for that one day; to paint the man, in short, as well as his features.”
—James Mcneill Whistler (18341903)
“Voluptuaries, consumed by their senses, always begin by flinging themselves with a great display of frenzy into an abyss. But they survive, they come to the surface again. And they develop a routine of the abyss: Its four oclock ... At five I have my abyss.”
—Colette [Sidonie Gabrielle Colette] (18731954)
“Nature centres into balls,
And her proud ephemerals,
Fast to surface and outside,
Scan the profile of the sphere;
Knew they what that signified,
A new genesis were here.”
—Ralph Waldo Emerson (18031882)