Plane (geometry)

Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface. A plane is the two dimensional analogue of a point (zero-dimensions), a line (one-dimension) and a solid (three-dimensions). Planes can arise as subspaces of some higher dimensional space, as with the walls of a room, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry.

When working exclusively in two-dimensional Euclidean space, the definite article is used, so, the plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory and graphing are performed in a two-dimensional space, or in other words, in the plane.

Read more about Plane (geometry):  Euclidean Geometry, Planes Embedded in 3-dimensional Euclidean Space, Planes in Various Areas of Mathematics, Topological and Differential Geometric Notions

Other articles related to "plane":

Plane (geometry) - Topological and Differential Geometric Notions
... The one-point compactification of the planeis homeomorphic to a sphere (see stereographic projection) the open disk is homeomorphic to a sphere with the "north pole" missing adding that point ... The projection from the Euclidean planeto a sphere without a point is a diffeomorphism and even a conformal map ... The planeitself is homeomorphic (and diffeomorphic) to an open disk ...

Famous quotes containing the word plane:

    Even though I had let them choose their own socks since babyhood, I was only beginning to learn to trust their adult judgment.. . . I had a sensation very much like the moment in an airplane when you realize that even if you stop holding the plane up by gripping the arms of your seat until your knuckles show white, the plane will stay up by itself. . . . To detach myself from my children . . . I had to achieve a condition which might be called loving objectivity.
    —Anonymous Parent of Adult Children. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 5 (1978)