Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Projection_(mathematics)> ?p ?o }
- Projection_(mathematics) abstract "In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent). The restriction to a subspace of a projection is also called a projection, even if the idempotence property is lost.An everyday example of a projection is the casting of shadows onto a plane (paper sheet). The projection of a point is its shadow on the paper sheet. The shadow of a point on the paper sheet is this point itself (idempotence). The shadow of a three-dimensional sphere is a circle. Originally, the notion of projection was introduced in Euclidean geometry to denote the projection of the Euclidean space of three dimensions onto a plane in it, like the shadow example. The two main projections of this kind are: The projection from a point onto a plane or central projection: If C is the point, called center of projection, the projection of a point P different from C is the intersection with the plane of the line CP. The point C and the points P such that the line CP is parallel to the plane do not have any image by the projection. The projection parallel to a direction D, onto a plane: The image of a point P is the intersection with the plane of the line parallel to D passing through P.The concept of projection in mathematics is a very old one, most likely having its roots in the phenomenon of the shadows cast by real world objects on the ground. This rudimentary idea was refined and abstracted, first in a geometric context and later in other branches of mathematics. Over time differing versions of the concept developed, but today, in a sufficiently abstract setting, we can unify these variations.In cartography, a map projection is a map of a part of the surface of the Earth onto a plane, which, in some cases, but not always, is the restriction of a projection in the above meaning. The 3D projections are also at the basis of the theory of perspective. The need for unifying the two kinds of projections and of defining the image by a central projection of any point different of the center of projection are at the origin of projective geometry. However, a projective transformation is a bijection of a projective space, a property not shared with the projections of this article.".
- Projection_(mathematics) thumbnail Proj-map.png?width=300.
- Projection_(mathematics) wikiPageExternalLink ABR2552.0001.001?rgn=works;view=toc;rgn1=author;q1=Craig.
- Projection_(mathematics) wikiPageID "3909097".
- Projection_(mathematics) wikiPageLength "7434".
- Projection_(mathematics) wikiPageOutDegree "57".
- Projection_(mathematics) wikiPageRevisionID "668441905".
- Projection_(mathematics) wikiPageWikiLink 3D_projection.
- Projection_(mathematics) wikiPageWikiLink Bijection.
- Projection_(mathematics) wikiPageWikiLink Cartesian_product.
- Projection_(mathematics) wikiPageWikiLink Cartography.
- Projection_(mathematics) wikiPageWikiLink Category:Mathematical_terminology.
- Projection_(mathematics) wikiPageWikiLink Category_(mathematics).
- Projection_(mathematics) wikiPageWikiLink Category_theory.
- Projection_(mathematics) wikiPageWikiLink Deformation_retract.
- Projection_(mathematics) wikiPageWikiLink Differential_topology.
- Projection_(mathematics) wikiPageWikiLink Direct_product_of_groups.
- Projection_(mathematics) wikiPageWikiLink Epimorphism.
- Projection_(mathematics) wikiPageWikiLink Equivalence_class.
- Projection_(mathematics) wikiPageWikiLink Equivalence_relation.
- Projection_(mathematics) wikiPageWikiLink Euclidean_geometry.
- Projection_(mathematics) wikiPageWikiLink Euclidean_space.
- Projection_(mathematics) wikiPageWikiLink Euclidean_vector.
- Projection_(mathematics) wikiPageWikiLink Fiber_bundle.
- Projection_(mathematics) wikiPageWikiLink Function_composition.
- Projection_(mathematics) wikiPageWikiLink Group_(mathematics).
- Projection_(mathematics) wikiPageWikiLink Homography.
- Projection_(mathematics) wikiPageWikiLink Homotopic.
- Projection_(mathematics) wikiPageWikiLink Homotopy.
- Projection_(mathematics) wikiPageWikiLink Idempotence.
- Projection_(mathematics) wikiPageWikiLink Idempotent.
- Projection_(mathematics) wikiPageWikiLink Injective_function.
- Projection_(mathematics) wikiPageWikiLink Linear_algebra.
- Projection_(mathematics) wikiPageWikiLink Linear_map.
- Projection_(mathematics) wikiPageWikiLink Linear_transformation.
- Projection_(mathematics) wikiPageWikiLink Map_(mathematics).
- Projection_(mathematics) wikiPageWikiLink Map_projection.
- Projection_(mathematics) wikiPageWikiLink Mathematical_structure.
- Projection_(mathematics) wikiPageWikiLink Mathematics.
- Projection_(mathematics) wikiPageWikiLink Morphism.
- Projection_(mathematics) wikiPageWikiLink Open_and_closed_maps.
- Projection_(mathematics) wikiPageWikiLink Open_map.
- Projection_(mathematics) wikiPageWikiLink Orthogonal_projection.
- Projection_(mathematics) wikiPageWikiLink Perspective_(graphical).
- Projection_(mathematics) wikiPageWikiLink Product_(category_theory).
- Projection_(mathematics) wikiPageWikiLink Product_topology.
- Projection_(mathematics) wikiPageWikiLink Projection_(linear_algebra).
- Projection_(mathematics) wikiPageWikiLink Projection_(set_theory).
- Projection_(mathematics) wikiPageWikiLink Projective_geometry.
- Projection_(mathematics) wikiPageWikiLink Projective_transformation.
- Projection_(mathematics) wikiPageWikiLink Restriction_(mathematics).
- Projection_(mathematics) wikiPageWikiLink Retract.
- Projection_(mathematics) wikiPageWikiLink Scalar_resolute.
- Projection_(mathematics) wikiPageWikiLink Set_(mathematics).
- Projection_(mathematics) wikiPageWikiLink Set_theory.
- Projection_(mathematics) wikiPageWikiLink Surjective.
- Projection_(mathematics) wikiPageWikiLink Surjective_function.
- Projection_(mathematics) wikiPageWikiLink Thomas_Craig_(mathematician).
- Projection_(mathematics) wikiPageWikiLink Topological_space.
- Projection_(mathematics) wikiPageWikiLink Topology.
- Projection_(mathematics) wikiPageWikiLink University_of_Michigan.
- Projection_(mathematics) wikiPageWikiLink Vector_(geometric).
- Projection_(mathematics) wikiPageWikiLink Vector_projection.
- Projection_(mathematics) wikiPageWikiLink File:Proj-map.png.
- Projection_(mathematics) wikiPageWikiLinkText "Projection (mathematics)".
- Projection_(mathematics) wikiPageWikiLinkText "Projection (mathematics)#Central projection".
- Projection_(mathematics) wikiPageWikiLinkText "Projection (mathematics)#canonical projection".
- Projection_(mathematics) wikiPageWikiLinkText "Projection".
- Projection_(mathematics) wikiPageWikiLinkText "central projection".
- Projection_(mathematics) wikiPageWikiLinkText "dropping".
- Projection_(mathematics) wikiPageWikiLinkText "project".
- Projection_(mathematics) wikiPageWikiLinkText "projected".
- Projection_(mathematics) wikiPageWikiLinkText "projecting".
- Projection_(mathematics) wikiPageWikiLinkText "projection map".
- Projection_(mathematics) wikiPageWikiLinkText "projection maps".
- Projection_(mathematics) wikiPageWikiLinkText "projection step".
- Projection_(mathematics) wikiPageWikiLinkText "projection".
- Projection_(mathematics) wikiPageWikiLinkText "projection-based".
- Projection_(mathematics) wikiPageWikiLinkText "projections".
- Projection_(mathematics) wikiPageWikiLinkText "projects".
- Projection_(mathematics) hasPhotoCollection Projection_(mathematics).
- Projection_(mathematics) wikiPageUsesTemplate Template:Anchor.
- Projection_(mathematics) wikiPageUsesTemplate Template:Merge_from.
- Projection_(mathematics) wikiPageUsesTemplate Template:No_references.
- Projection_(mathematics) wikiPageUsesTemplate Template:Reflist.
- Projection_(mathematics) wikiPageUsesTemplate Template:Visible_anchor.
- Projection_(mathematics) subject Category:Mathematical_terminology.
- Projection_(mathematics) hypernym Mapping.
- Projection_(mathematics) type Work.
- Projection_(mathematics) comment "In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent). The restriction to a subspace of a projection is also called a projection, even if the idempotence property is lost.An everyday example of a projection is the casting of shadows onto a plane (paper sheet). The projection of a point is its shadow on the paper sheet.".
- Projection_(mathematics) label "Projection (mathematics)".
- Projection_(mathematics) sameAs Proyección_(matemáticas).
- Projection_(mathematics) sameAs Projecteur_(mathématiques).
- Projection_(mathematics) sameAs 射影.
- Projection_(mathematics) sameAs Projekcija_(geometrija).
- Projection_(mathematics) sameAs Projectie_(wiskunde).
- Projection_(mathematics) sameAs Projeksjon_i_matematikk.
- Projection_(mathematics) sameAs Rzut_(geometria).
- Projection_(mathematics) sameAs Projeção_(matemática).
- Projection_(mathematics) sameAs m.0b69v_.