**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":

... The one-point compactification of the

**plane**is 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

**plane**to a sphere without a point is a diffeomorphism and even a conformal map ... The

**plane**itself 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)