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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 ...
Aside from the Orthographic, six standard principal views (Front; Right Side; Left Side; Top; Bottom; Rear), descriptive geometry strives to yield four basic solution views: the true length of a line (i.e., full size, not foreshortened), the point view (end view) of a line, the true shape of a plane (i.e., full size to scale, or not ...
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 .
The most basic example is the flat Euclidean plane, an idealization of a flat surface in physical space such as a sheet of paper or a chalkboard. On the Euclidean plane, any two points can be joined by a unique straight line along which the distance can be measured.
For example, the dimension of a point is zero; the dimension of a line is one, as a point can move on a line in only one direction (or its opposite); the dimension of a plane is two, etc. The dimension is an intrinsic property of an object, in the sense that it is independent of the dimension of the space in which the object is or can be embedded.
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The flats in a plane (two-dimensional space) are points, lines, and the plane itself; the flats in three-dimensional space are points, lines, planes, and the space itself. The definition of flat excludes non-straight curves and non-planar surfaces, which are subspaces having different notions of distance: arc length and geodesic length ...
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