Matches in DBpedia 2016-04 for { <http://wikidata.dbpedia.org/resource/Q5958478> ?p ?o }
Showing triples 1 to 19 of
19
with 100 triples per page.
- Q5958478 subject Q7164757.
- Q5958478 subject Q8824657.
- Q5958478 abstract "In geometry, any hyperplane H of a projective space P may be taken as a hyperplane at infinity. Then the set complement P ∖ H is called an affine space. For instance, if (x1, ..., xn, xn+1) are homogeneous coordinates for n-dimensional projective space, then the equation xn+1 = 0 defines a hyperplane at infinity for the n-dimensional affine space with coordinates (x1, ..., xn). H is also called the ideal hyperplane.Similarly, starting from an affine space A, every class of parallel lines can be associated with a point at infinity. The union over all classes of parallels constitute the points of the hyperplane at infinity. Adjoining the points of this hyperplane (called ideal points) to A converts it into an n-dimensional projective space, such as the real projective space RPn.By adding these ideal points, the entire affine space A is completed to a projective space P, which may be called the projective completion of A. Each affine subspace S of A is completed to a projective subspace of P by adding to S all the ideal points corresponding to the directions of the lines contained in S. The resulting projective subspaces are often called affine subspaces of the projective space P, as opposed to the infinite or ideal subspaces, which are the subspaces of the hyperplane at infinity (however, they are projective spaces, not affine spaces).In the projective space, each projective subspace of dimension k intersects the ideal hyperplane in a projective subspace "at infinity" whose dimension is k − 1.A pair of non-parallel affine hyperplanes intersect at an affine subspace of dimension n − 2, but a parallel pair of affine hyperplanes intersect at a projective subspace of the ideal hyperplane (the intersection lies on the ideal hyperplane). Thus, parallel hyperplanes, which did not meet in the affine space, intersect in the projective completion due to the addition of the hyperplane at infinity.".
- Q5958478 wikiPageWikiLink Q1191139.
- Q5958478 wikiPageWikiLink Q185359.
- Q5958478 wikiPageWikiLink Q2130665.
- Q5958478 wikiPageWikiLink Q242767.
- Q5958478 wikiPageWikiLink Q382698.
- Q5958478 wikiPageWikiLink Q528525.
- Q5958478 wikiPageWikiLink Q53875.
- Q5958478 wikiPageWikiLink Q657586.
- Q5958478 wikiPageWikiLink Q7164757.
- Q5958478 wikiPageWikiLink Q7201011.
- Q5958478 wikiPageWikiLink Q8087.
- Q5958478 wikiPageWikiLink Q877775.
- Q5958478 wikiPageWikiLink Q8824657.
- Q5958478 wikiPageWikiLink Q912887.
- Q5958478 comment "In geometry, any hyperplane H of a projective space P may be taken as a hyperplane at infinity. Then the set complement P ∖ H is called an affine space. For instance, if (x1, ..., xn, xn+1) are homogeneous coordinates for n-dimensional projective space, then the equation xn+1 = 0 defines a hyperplane at infinity for the n-dimensional affine space with coordinates (x1, ..., xn).".
- Q5958478 label "Hyperplane at infinity".