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The three possible plane-line relationships in three dimensions. (Shown in each case is only a portion of the plane, which extends infinitely far.) In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. It is the entire line if that line is embedded in the plane, and is ...
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. [9] Such a drawing is called a plane graph or planar embedding of the graph.
As any line in this extension of σ corresponds to a plane through O, and since any pair of such planes intersects in a line through O, one can conclude that any pair of lines in the extension intersect: the point of intersection lies where the plane intersection meets σ or the line at infinity. Thus the axiom of projective geometry, requiring ...
Reflections, or mirror isometries, denoted by F c,v, where c is a point in the plane and v is a unit vector in R 2. (F is for "flip".) have the effect of reflecting the point p in the line L that is perpendicular to v and that passes through c. The line L is called the reflection axis or the associated mirror.
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 ...
In geometry, a motion is an isometry of a metric space. For instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping associating congruent figures is a motion. [1] More generally, the term motion is a synonym for surjective isometry in metric geometry, [2] including elliptic geometry and hyperbolic ...
Comparison of several types of graphical projection, including elevation and plan views. To render each such picture, a ray of sight (also called a projection line, projection ray or line of sight) towards the object is chosen, which determines on the object various points of interest (for instance, the points that are visible when looking at the object along the ray of sight); those points of ...
In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons , the cells of the arrangement, line segments and rays , the edges of the arrangement, and points where two or more lines cross, the vertices of the arrangement.