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- 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 wikiPageRevisionID "581854011".
- Ruled_surface first "V.A.".
- Ruled_surface hasPhotoCollection Ruled_surface.
- 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 subject Category:Algebraic_surfaces.
- Ruled_surface subject Category:Analytic_geometry.
- Ruled_surface subject Category:Complex_surfaces.
- Ruled_surface subject Category:Differential_geometry.
- Ruled_surface subject Category:Differential_geometry_of_surfaces.
- Ruled_surface subject Category:Geometric_shapes.
- Ruled_surface subject Category:Surfaces.
- Ruled_surface type AlgebraicSurfaces.
- Ruled_surface type Artifact100021939.
- Ruled_surface type ComplexSurfaces.
- Ruled_surface type Object100002684.
- Ruled_surface type PhysicalEntity100001930.
- Ruled_surface type Surface104362025.
- Ruled_surface type Surfaces.
- Ruled_surface type Whole100003553.
- Ruled_surface comment "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.".
- Ruled_surface label "Powierzchnia prostokreślna".
- Ruled_surface label "Regelfläche".
- Ruled_surface label "Regeloppervlak".
- Ruled_surface label "Ruled surface".
- Ruled_surface label "Superficie reglada".
- Ruled_surface label "Superficie rigata".
- Ruled_surface label "Superfície regrada".
- Ruled_surface label "Surface réglée".
- Ruled_surface label "Линейчатая поверхность".
- Ruled_surface label "سطح مسطر".
- Ruled_surface sameAs Přímková_plocha.
- Ruled_surface sameAs Regelfläche.
- Ruled_surface sameAs Superficie_reglada.
- Ruled_surface sameAs Surface_réglée.
- Ruled_surface sameAs Superficie_rigata.
- Ruled_surface sameAs Regeloppervlak.
- Ruled_surface sameAs Powierzchnia_prostokreślna.
- Ruled_surface sameAs Superfície_regrada.
- Ruled_surface sameAs m.0348cr.
- Ruled_surface sameAs Q840376.
- Ruled_surface sameAs Q840376.
- Ruled_surface sameAs Ruled_surface.
- Ruled_surface wasDerivedFrom Ruled_surface?oldid=581854011.
- Ruled_surface depiction Ruled_hyperboloid.jpg.
- Ruled_surface isPrimaryTopicOf Ruled_surface.
