Ads
related to: points lines and planes pptelements.envato.com has been visited by 100K+ users in the past month
amazon.com has been visited by 1M+ users in the past month
aippt.com has been visited by 10K+ users in the past month
Search results
Results From The WOW.Com Content Network
Steinitz (1894) [8] has shown that n 3-configurations (incidence structures with n points and n lines, three points per line and three lines through each point) are either realizable or require the use of only one curved line in their representations. [9] The Fano plane is the unique (7 3) and the Möbius–Kantor configuration is the unique (8 3).
A generalized n-gon contains no ordinary m-gon for 2 ≤ m < n and for every pair of objects (two points, two lines or a point and a line) there is an ordinary n-gon that contains them both. Generalized 3-gons are projective planes. Generalized 4-gons are called generalized quadrangles.
Although it may be embedded in two dimensions, the Desargues configuration has a very simple construction in three dimensions: for any configuration of five planes in general position in Euclidean space, the ten points where three planes meet and the ten lines formed by the intersection of two of the planes together form an instance of the configuration. [2]
Given a point and a line, there is a unique line which contains the point and is parallel to the line. Parallelism is an equivalence relation on the lines of an affine plane. Since no concepts other than those involving the relationship between points and lines are involved in the axioms, an affine plane is an object of study belonging to ...
In a projective plane a statement involving points, lines and incidence between them that is obtained from another such statement by interchanging the words "point" and "line" and making whatever grammatical adjustments that are necessary, is called the plane dual statement of the first. The plane dual statement of "Two points are on a unique ...
The lines of a compact topological plane with a 2-dimensional point space form a family of curves homeomorphic to a circle, and this fact characterizes these planes among the topological projective planes. [10] Equivalently, the point space is a surface.