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In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...
A Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane. The set of the ordered pairs of real numbers (the real coordinate plane), equipped with the dot product, is often called the Euclidean plane or standard Euclidean plane, since every Euclidean plane is isomorphic to it.
A plane segment or planar region (or simply "plane", in lay use) is a planar surface region; it is analogous to a line segment. A bivector is an oriented plane segment, analogous to directed line segments. [a] A face is a plane segment bounding a solid object. [1] A slab is a region bounded by two parallel planes.
The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language. [1]
A vector plane is an affine plane whose points, called vectors, include a special designated origin or zero vector. Vectors can be added together or scaled by a number, and optionally have a Euclidean, Lorentzian, or Galilean concept of distance.
A line can lie in a given plane, intersect that plane in a unique point, or be parallel to the plane. In the last case, there will be lines in the plane that are parallel to the given line. A hyperplane is a subspace of one dimension less than the dimension of the full space. The hyperplanes of a three-dimensional space are the two-dimensional ...
Euclidean plane geometry (11 C, 96 P) G. Planar graphs (1 C, 88 P) T. ... Pages in category "Planes (geometry)" The following 51 pages are in this category, out of 51 ...
Quadrant (plane geometry) 25 languages. ... The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, ...