Duocylinder (original) (raw)
The duocylinder, also called the double cylinder or the bidisc, is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of respective radii r1 and r2: It is analogous to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment. But unlike the cylinder, both hypersurfaces (of a regular duocylinder) are congruent. Its dual is a duospindle, constructed from two circles, one at the XY plane and the other in the ZW plane.
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| dbo:abstract | The duocylinder, also called the double cylinder or the bidisc, is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of respective radii r1 and r2: It is analogous to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment. But unlike the cylinder, both hypersurfaces (of a regular duocylinder) are congruent. Its dual is a duospindle, constructed from two circles, one at the XY plane and the other in the ZW plane. (en) El duocilindro es un objeto de revolución del espacio tetradimensional. Se describe como el producto cartesiano de dos discos definidos sobre los planos XY y ZW del espacio tetradimensional euclídeo. (es) Le double cylindre, ou duocylindre, est un objet géométrique défini comme le produit cartésien de deux disques de rayons respectifs r1 et r2. On peut le représenter comme une région de l'espace euclidien à quatre dimensions délimitée par deux hypersurfaces : dans un repère cartésien convenable, c'est l'ensemble des points. Il constitue l'une des généralisations du cylindre de l'espace usuel, c'est-à-dire du produit cartésien d'un disque et d'un segment ; d'autres généralisations naturelles sont le cylindre sphérique et le cylindre cubique. Dans la représentation canonique du double cylindre, les deux hypersurfaces qui le délimitent sont congruentes et ont pour intersection un tore de Clifford, appelé arête du double cylindre. (fr) |
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| dbo:wikiPageExternalLink | https://web.archive.org/web/20030121092141/http:/etext.lib.virginia.edu/etcbin/toccer-new2%3Fid=ManFour.sgm&images=images%2Fmodeng&data=%2Ftexts%2Fenglish%2Fmodeng%2Fparsed&tag=public&part=all https://web.archive.org/web/20141201023452/http:/www.bayarea.net/~kins/thomas_briggs/ http://eusebeia.dyndns.org/4d/duocylinder.html http://tetraspace.alkaline.org/shapes/rotachora.htm http://tetraspace.alkaline.org/shapes/rotatopeclass.htm |
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| rdfs:comment | The duocylinder, also called the double cylinder or the bidisc, is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of respective radii r1 and r2: It is analogous to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment. But unlike the cylinder, both hypersurfaces (of a regular duocylinder) are congruent. Its dual is a duospindle, constructed from two circles, one at the XY plane and the other in the ZW plane. (en) El duocilindro es un objeto de revolución del espacio tetradimensional. Se describe como el producto cartesiano de dos discos definidos sobre los planos XY y ZW del espacio tetradimensional euclídeo. (es) Le double cylindre, ou duocylindre, est un objet géométrique défini comme le produit cartésien de deux disques de rayons respectifs r1 et r2. On peut le représenter comme une région de l'espace euclidien à quatre dimensions délimitée par deux hypersurfaces : dans un repère cartésien convenable, c'est l'ensemble des points. Il constitue l'une des généralisations du cylindre de l'espace usuel, c'est-à-dire du produit cartésien d'un disque et d'un segment ; d'autres généralisations naturelles sont le cylindre sphérique et le cylindre cubique. (fr) |
| rdfs:label | Duocilindro (es) Double cylindre (fr) Duocylinder (en) |
| rdfs:seeAlso | dbr:Polydisc |
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