Search results
Results from the WOW.Com Content Network
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 ...
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.
This definition of covering dimension can be extended from the class of normal spaces to all Tychonoff spaces merely by replacing the term "open" in the definition by the term "functionally open". An inductive dimension may be defined inductively as follows. Consider a discrete set of points (such as a finite collection of points) to be 0 ...
In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted or . It is a geometric space in which two real numbers are required to determine the position of each point . It is an affine space , which includes in particular the concept of parallel lines .
In a Cartesian plane, one can define canonical representatives of certain geometric figures, such as the unit circle (with radius equal to the length unit, and center at the origin), the unit square (whose diagonal has endpoints at (0, 0) and (1, 1)), the unit hyperbola, and so on. The two axes divide the plane into four right angles, called ...
The complex plane is two-dimensional when considered to be formed from real-number coordinates, but one-dimensional in terms of complex-number coordinates. A two-dimensional complex space – such as the two-dimensional complex coordinate space , the complex projective plane , or a complex surface – has two complex dimensions, which can ...
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.
A quasi-isometry is a map that preserves the "large-scale structure" of a metric space. Quasi-isometries need not be continuous. Quasi-isometries need not be continuous. For example, R 2 {\displaystyle \mathbb {R} ^{2}} and its subspace Z 2 {\displaystyle \mathbb {Z} ^{2}} are quasi-isometric, even though one is connected and the other is discrete.