Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Ruled_surface> ?p ?o }
- Ruled_surface abstract "In geometry, a surface S is ruled (also called a scroll) if through every point of S there is a straight line that lies on S. The most familiar examples (illustrated here in three-dimensional Euclidean space) are the plane and the curved surface of a cylinder or cone. Other examples are a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space.A ruled surface can always be described (at least locally) as the set of points swept by a moving straight line. For example, a cone is formed by keeping one point of a line fixed whilst moving another point along a circle.A surface is doubly ruled if through every one of its points there are two distinct lines that lie on the surface. The hyperbolic paraboloid and the hyperboloid of one sheet are doubly ruled surfaces. The plane is the only surface which contains at least three distinct lines through each of its points.The properties of being ruled or doubly ruled are preserved by projective maps, and therefore are concepts of projective geometry. In algebraic geometry ruled surfaces are sometimes considered to be surfaces in affine or projective space over a field, but they are also sometimes considered as abstract algebraic surfaces without an embedding into affine or projective space, in which case \"straight line\" is understood to mean an affine or projective line.".
- Ruled_surface thumbnail Ruled_hyperboloid.jpg?width=300.
- Ruled_surface wikiPageExternalLink Ruled_Surfaces.
- Ruled_surface wikiPageExternalLink developable.
- Ruled_surface wikiPageID "705158".
- Ruled_surface wikiPageLength "9082".
- Ruled_surface wikiPageOutDegree "76".
- Ruled_surface wikiPageRevisionID "700606912".
- Ruled_surface wikiPageWikiLink Birational_geometry.
- Ruled_surface wikiPageWikiLink Cambridge_University_Press.
- Ruled_surface wikiPageWikiLink Category:Algebraic_surfaces.
- Ruled_surface wikiPageWikiLink Category:Analytic_geometry.
- Ruled_surface wikiPageWikiLink Category:Complex_surfaces.
- Ruled_surface wikiPageWikiLink Category:Differential_geometry.
- Ruled_surface wikiPageWikiLink Category:Differential_geometry_of_surfaces.
- Ruled_surface wikiPageWikiLink Category:Geometric_shapes.
- Ruled_surface wikiPageWikiLink Category:Surfaces.
- Ruled_surface wikiPageWikiLink Ciechanów.
- Ruled_surface wikiPageWikiLink Circle.
- Ruled_surface wikiPageWikiLink Complete_metric_space.
- Ruled_surface wikiPageWikiLink Cone.
- Ruled_surface wikiPageWikiLink Conical_surface.
- Ruled_surface wikiPageWikiLink Conoid.
- Ruled_surface wikiPageWikiLink Cooling_channel.
- Ruled_surface wikiPageWikiLink Cooling_tower.
- Ruled_surface wikiPageWikiLink Cremona.
- Ruled_surface wikiPageWikiLink Curve.
- Ruled_surface wikiPageWikiLink Cylinder_(geometry).
- Ruled_surface wikiPageWikiLink Developable_surface.
- Ruled_surface wikiPageWikiLink Didcot_power_stations.
- Ruled_surface wikiPageWikiLink Differential_geometry_of_surfaces.
- Ruled_surface wikiPageWikiLink Ellipse.
- Ruled_surface wikiPageWikiLink Enriques–Kodaira_classification.
- Ruled_surface wikiPageWikiLink Euclidean_space.
- Ruled_surface wikiPageWikiLink Fibration.
- Ruled_surface wikiPageWikiLink Generalized_helicoid.
- Ruled_surface wikiPageWikiLink Geometry.
- Ruled_surface wikiPageWikiLink Gridshell.
- Ruled_surface wikiPageWikiLink Helicoid.
- Ruled_surface wikiPageWikiLink Hirzebruch_surface.
- Ruled_surface wikiPageWikiLink Homography.
- Ruled_surface wikiPageWikiLink Hyperboloid.
- Ruled_surface wikiPageWikiLink Hyperboloid_structure.
- Ruled_surface wikiPageWikiLink Kobe.
- Ruled_surface wikiPageWikiLink Kobe_Port_Tower.
- Ruled_surface wikiPageWikiLink Kodaira_dimension.
- Ruled_surface wikiPageWikiLink Latticework.
- Ruled_surface wikiPageWikiLink List_of_surfaces.
- Ruled_surface wikiPageWikiLink Möbius_strip.
- Ruled_surface wikiPageWikiLink Nozzle.
- Ruled_surface wikiPageWikiLink Paraboloid.
- Ruled_surface wikiPageWikiLink Parametric_equation.
- Ruled_surface wikiPageWikiLink Parametric_model.
- Ruled_surface wikiPageWikiLink Plane_(geometry).
- Ruled_surface wikiPageWikiLink Pointed_hat.
- Ruled_surface wikiPageWikiLink Projective_geometry.
- Ruled_surface wikiPageWikiLink Projective_plane.
- Ruled_surface wikiPageWikiLink Projective_space.
- Ruled_surface wikiPageWikiLink RM-81_Agena.
- Ruled_surface wikiPageWikiLink Rational_normal_curve.
- Ruled_surface wikiPageWikiLink Rational_normal_scroll.
- Ruled_surface wikiPageWikiLink Right_conoid.
- Ruled_surface wikiPageWikiLink Rocket_engine.
- Ruled_surface wikiPageWikiLink Saddle_roof.
- Ruled_surface wikiPageWikiLink Sagrada_Família.
- Ruled_surface wikiPageWikiLink Shukhov_Tower.
- Ruled_surface wikiPageWikiLink Skew_lines.
- Ruled_surface wikiPageWikiLink Surface.
- Ruled_surface wikiPageWikiLink Tangent_developable.
- Ruled_surface wikiPageWikiLink Torrazzo_of_Cremona.
- Ruled_surface wikiPageWikiLink Torus.
- Ruled_surface wikiPageWikiLink Unit_sphere.
- Ruled_surface wikiPageWikiLink Unit_vector.
- Ruled_surface wikiPageWikiLink Warsaw.
- Ruled_surface wikiPageWikiLink Warszawa_Ochota_train_station.
- Ruled_surface wikiPageWikiLink Waste_container.
- Ruled_surface wikiPageWikiLink File:Helicoid.svg.
- Ruled_surface wikiPageWikiLink File:Hyperbolic-paraboloid.svg.
- Ruled_surface wikiPageWikiLink File:Ruled_hyperboloid.jpg.
- Ruled_surface wikiPageWikiLinkText "Ruled surface".
- Ruled_surface wikiPageWikiLinkText "doubly ruled surface".
- Ruled_surface wikiPageWikiLinkText "doubly-ruled surface".
- Ruled_surface wikiPageWikiLinkText "generators of the ruling".
- Ruled_surface wikiPageWikiLinkText "lines on a hyperboloid".
- Ruled_surface wikiPageWikiLinkText "ruled geometrical forms".
- Ruled_surface wikiPageWikiLinkText "ruled geometry".
- Ruled_surface wikiPageWikiLinkText "ruled surface".
- Ruled_surface wikiPageWikiLinkText "ruled surfaces".
- Ruled_surface wikiPageWikiLinkText "ruled".
- Ruled_surface wikiPageWikiLinkText "ruled-surface".
- Ruled_surface first "V.A.".
- Ruled_surface id "R/r082790".
- Ruled_surface id "RuledSurface".
- Ruled_surface last "Iskovskikh".
- Ruled_surface title "Ruled Surface".
- Ruled_surface title "Ruled surface".
- Ruled_surface wikiPageUsesTemplate Template:Citation.
- Ruled_surface wikiPageUsesTemplate Template:Doi.
- Ruled_surface wikiPageUsesTemplate Template:Harv.
- Ruled_surface wikiPageUsesTemplate Template:Main.