Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Projective_geometry> ?p ?o }
- Projective_geometry abstract "In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, in a given dimension, and that geometric transformations are permitted that move the extra points (called "points at infinity") to traditional points, and vice versa.Properties meaningful in projective geometry are respected by this new idea of transformation, which is more radical in its effects than expressible by a transformation matrix and translations (the affine transformations). The first issue for geometers is what kind of geometric language is adequate to the novel situation. It is not possible to talk about angles in projective geometry as it is in Euclidean geometry, because angle is an example of a concept not invariant under projective transformations, as is seen clearly in perspective drawing. One source for projective geometry was indeed the theory of perspective. Another difference from elementary geometry is the way in which parallel lines can be said to meet in a point at infinity, once the concept is translated into projective geometry's terms. Again this notion has an intuitive basis, such as railway tracks meeting at the horizon in a perspective drawing. See projective plane for the basics of projective geometry in two dimensions.While the ideas were available earlier, projective geometry was mainly a development of the nineteenth century. A huge body of research made it the most representative field of geometry of that time. This was the theory of complex projective space, since the coordinates used (homogeneous coordinates) were complex numbers. Several major strands of more abstract mathematics (including invariant theory, the Italian school of algebraic geometry, and Felix Klein's Erlangen programme leading to the study of the classical groups) built on projective geometry. It was also a subject with a large number of practitioners for its own sake, under the banner of synthetic geometry. Another field that emerged from axiomatic studies of projective geometry is finite geometry.The field of projective geometry is itself now divided into many research subfields, two examples of which are projective algebraic geometry (the study of projective varieties) and projective differential geometry (the study of differential invariants of the projective transformations).".
- Projective_geometry thumbnail Theoreme_fondamental_geometrie_projective.PNG?width=300.
- Projective_geometry wikiPageExternalLink summary?doi=10.1.1.17.1329.
- Projective_geometry wikiPageExternalLink isprs96.html.
- Projective_geometry wikiPageExternalLink burali-forti_-_diff._geom._following_grassmann.pdf.
- Projective_geometry wikiPageExternalLink burali-forti_-_grassman_and_proj._geom..pdf.
- Projective_geometry wikiPageExternalLink kummer_-_rectilinear_ray_systems.pdf.
- Projective_geometry wikiPageExternalLink pasch_-_focal_and_singularity_surfaces.pdf.
- Projective_geometry wikiPageExternalLink projective.pdf.
- Projective_geometry wikiPageExternalLink ?p=262.
- Projective_geometry wikiPageExternalLink projective_geometry.html.
- Projective_geometry wikiPageID "243849".
- Projective_geometry wikiPageLength "32175".
- Projective_geometry wikiPageOutDegree "185".
- Projective_geometry wikiPageRevisionID "682365325".
- Projective_geometry wikiPageWikiLink Affine_geometry.
- Projective_geometry wikiPageWikiLink Affine_transformation.
- Projective_geometry wikiPageWikiLink Alessandro_Padoa.
- Projective_geometry wikiPageWikiLink Alfred_Clebsch.
- Projective_geometry wikiPageWikiLink Alfred_North_Whitehead.
- Projective_geometry wikiPageWikiLink Algebra.
- Projective_geometry wikiPageWikiLink Algebraic_curve.
- Projective_geometry wikiPageWikiLink Algebraic_geometry.
- Projective_geometry wikiPageWikiLink Algebraic_topology.
- Projective_geometry wikiPageWikiLink Algebraic_variety.
- Projective_geometry wikiPageWikiLink Analytic_geometry.
- Projective_geometry wikiPageWikiLink Angle.
- Projective_geometry wikiPageWikiLink Axiom.
- Projective_geometry wikiPageWikiLink Axioms.
- Projective_geometry wikiPageWikiLink Beltrami–Klein_model.
- Projective_geometry wikiPageWikiLink Bernhard_Riemann.
- Projective_geometry wikiPageWikiLink Blaise_Pascal.
- Projective_geometry wikiPageWikiLink Category:Projective_geometry.
- Projective_geometry wikiPageWikiLink Chern_class.
- Projective_geometry wikiPageWikiLink Classical_group.
- Projective_geometry wikiPageWikiLink Classical_groups.
- Projective_geometry wikiPageWikiLink Clebsch.
- Projective_geometry wikiPageWikiLink Compass_(drafting).
- Projective_geometry wikiPageWikiLink Compass_(drawing_tool).
- Projective_geometry wikiPageWikiLink Complete_quadrangle.
- Projective_geometry wikiPageWikiLink Complex_number.
- Projective_geometry wikiPageWikiLink Complex_projective_space.
- Projective_geometry wikiPageWikiLink Configuration_(geometry).
- Projective_geometry wikiPageWikiLink Conic.
- Projective_geometry wikiPageWikiLink Conic_section.
- Projective_geometry wikiPageWikiLink Conic_sections.
- Projective_geometry wikiPageWikiLink Corrado_Segre.
- Projective_geometry wikiPageWikiLink Cross-ratio.
- Projective_geometry wikiPageWikiLink David_Hilbert.
- Projective_geometry wikiPageWikiLink Desargues_Theorem.
- Projective_geometry wikiPageWikiLink Desargues_theorem.
- Projective_geometry wikiPageWikiLink Differential_geometry.
- Projective_geometry wikiPageWikiLink Dimension.
- Projective_geometry wikiPageWikiLink Division_ring.
- Projective_geometry wikiPageWikiLink Duality_(projective_geometry).
- Projective_geometry wikiPageWikiLink Ellipse.
- Projective_geometry wikiPageWikiLink Elliptic_geometry.
- Projective_geometry wikiPageWikiLink Enumerative_geometry.
- Projective_geometry wikiPageWikiLink Ergebnisse_der_Mathematik_und_ihrer_Grenzgebiete.
- Projective_geometry wikiPageWikiLink Erlangen_program.
- Projective_geometry wikiPageWikiLink Erlangen_programme.
- Projective_geometry wikiPageWikiLink Euclidean_geometry.
- Projective_geometry wikiPageWikiLink Euclidean_space.
- Projective_geometry wikiPageWikiLink Fano_plane.
- Projective_geometry wikiPageWikiLink Federigo_Enriques.
- Projective_geometry wikiPageWikiLink Felix_Klein.
- Projective_geometry wikiPageWikiLink Filippo_Brunelleschi.
- Projective_geometry wikiPageWikiLink Finite_geometry.
- Projective_geometry wikiPageWikiLink Finite_projective_geometry.
- Projective_geometry wikiPageWikiLink Francesco_Severi.
- Projective_geometry wikiPageWikiLink Fundamental_theorem_of_projective_geometry.
- Projective_geometry wikiPageWikiLink Gaspard_Monge.
- Projective_geometry wikiPageWikiLink Geometric_transformation.
- Projective_geometry wikiPageWikiLink Geometry.
- Projective_geometry wikiPageWikiLink Gino_Fano.
- Projective_geometry wikiPageWikiLink Girard_Desargues.
- Projective_geometry wikiPageWikiLink Giuseppe_Peano.
- Projective_geometry wikiPageWikiLink Grassmannian.
- Projective_geometry wikiPageWikiLink Grassmann–Cayley_algebra.
- Projective_geometry wikiPageWikiLink Group_(mathematics).
- Projective_geometry wikiPageWikiLink Gérard_Desargues.
- Projective_geometry wikiPageWikiLink H._F._Baker.
- Projective_geometry wikiPageWikiLink H._S._M._Coxeter.
- Projective_geometry wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Projective_geometry wikiPageWikiLink Higher_dimension.
- Projective_geometry wikiPageWikiLink Homogeneous_coordinates.
- Projective_geometry wikiPageWikiLink Homography.
- Projective_geometry wikiPageWikiLink Howard_Eves.
- Projective_geometry wikiPageWikiLink Hyperbola.
- Projective_geometry wikiPageWikiLink Hyperbolic_geometry.
- Projective_geometry wikiPageWikiLink Hyperbolic_space.
- Projective_geometry wikiPageWikiLink Hyperplane.
- Projective_geometry wikiPageWikiLink Hyperplanes.
- Projective_geometry wikiPageWikiLink Incidence_(geometry).
- Projective_geometry wikiPageWikiLink Incidence_(mathematics).
- Projective_geometry wikiPageWikiLink Incidence_geometry.
- Projective_geometry wikiPageWikiLink Incidence_structure.
- Projective_geometry wikiPageWikiLink Infinity.
- Projective_geometry wikiPageWikiLink Invariant_(mathematics).
- Projective_geometry wikiPageWikiLink Invariant_theory.