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- Catalan_surface abstract "In geometry, a Catalan surface, named after the Belgian mathematician Eugène Charles Catalan, is a ruled surface all of whose rulings are parallel to a fixed plane. The vector equation of a Catalan surface is given by r = s(u) + v L(u),where r = s(u) is the space curve and L(u) is the unit vector of the ruling at u = u. All the vectors L(u) are parallel to the same plane, called the directrix plane of the surface. This can be characterized by the condition: the mixed product [L(u), L' (u), L" (u)] = 0.[1]The parametric equations of the Catalan surface are [2]If all the rulings of a Catalan surface intersect a fixed line, then the surface is called a conoid.Catalan proved that the helicoid and the plane were the only ruled minimal surfaces.".
- Catalan_surface thumbnail Catalan_surface.gif?width=300.
- Catalan_surface wikiPageExternalLink books?id=K31Nzi_xhoQC&pg=PA277&dq=conoid+maple&lr=&ei=B9hvSs_qKYzSkASR8c3XDg.
- Catalan_surface wikiPageExternalLink v=onepage&q=catalan%20surface&f=false.
- Catalan_surface wikiPageExternalLink product_detail.jsf?catno=C4487&isbn=0000000000000.
- Catalan_surface wikiPageExternalLink catalan.shtml.
- Catalan_surface wikiPageID "23808629".
- Catalan_surface wikiPageRevisionID "553191039".
- Catalan_surface hasPhotoCollection Catalan_surface.
- Catalan_surface id "p/c020710".
- Catalan_surface title "Catalan surface".
- Catalan_surface subject Category:Geometric_shapes.
- Catalan_surface subject Category:Surfaces.
- Catalan_surface type Artifact100021939.
- Catalan_surface type Object100002684.
- Catalan_surface type PhysicalEntity100001930.
- Catalan_surface type Surface104362025.
- Catalan_surface type Surfaces.
- Catalan_surface type Whole100003553.
- Catalan_surface comment "In geometry, a Catalan surface, named after the Belgian mathematician Eugène Charles Catalan, is a ruled surface all of whose rulings are parallel to a fixed plane. The vector equation of a Catalan surface is given by r = s(u) + v L(u),where r = s(u) is the space curve and L(u) is the unit vector of the ruling at u = u. All the vectors L(u) are parallel to the same plane, called the directrix plane of the surface.".
- Catalan_surface label "Catalan surface".
- Catalan_surface label "سطح كاتالان".
- Catalan_surface sameAs m.06_vhb2.
- Catalan_surface sameAs Q4119065.
- Catalan_surface sameAs Q4119065.
- Catalan_surface sameAs Catalan_surface.
- Catalan_surface wasDerivedFrom Catalan_surface?oldid=553191039.
- Catalan_surface depiction Catalan_surface.gif.
- Catalan_surface isPrimaryTopicOf Catalan_surface.