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- Real_projective_plane abstract "In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold, that is, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has basic applications to geometry, since the common construction of the real projective plane is as the space of lines in R3 passing through the origin. The plane is also often described topologically, in terms of a construction based on the Möbius strip: if one could glue the (single) edge of the Möbius strip to itself in the correct direction, one would obtain the projective plane. (This cannot be done in three-dimensional space.) Equivalently, gluing a disk along the boundary of the Möbius strip gives the projective plane. Topologically, it has Euler characteristic 1, hence a demigenus (non-orientable genus, Euler genus) of 1.Since the Möbius strip, in turn, can be constructed from a square by gluing two of its sides together, the real projective plane can thus be represented as a unit square (that is, [0,1] × [0,1] ) with its sides identified by the following equivalence relations:(0, y) ~ (1, 1 − y) for 0 ≤ y ≤ 1 and (x, 0) ~ (1 − x, 1) for 0 ≤ x ≤ 1,as in the leftmost diagram on the right.".
- Real_projective_plane thumbnail ProjectivePlaneAsSquare.svg?width=300.
- Real_projective_plane wikiPageExternalLink rptwo.htm.
- Real_projective_plane wikiPageExternalLink Demiralp-2009-CLF.pdf.
- Real_projective_plane wikiPageExternalLink watch?v=lDqmaPEjJpk.
- Real_projective_plane wikiPageID "411325".
- Real_projective_plane wikiPageRevisionID "590056131".
- Real_projective_plane hasPhotoCollection Real_projective_plane.
- Real_projective_plane title "Real Projective Plane".
- Real_projective_plane urlname "RealProjectivePlane".
- Real_projective_plane subject Category:Geometric_topology.
- Real_projective_plane subject Category:Surfaces.
- Real_projective_plane type Artifact100021939.
- Real_projective_plane type Object100002684.
- Real_projective_plane type PhysicalEntity100001930.
- Real_projective_plane type Surface104362025.
- Real_projective_plane type Surfaces.
- Real_projective_plane type Whole100003553.
- Real_projective_plane comment "In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold, that is, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has basic applications to geometry, since the common construction of the real projective plane is as the space of lines in R3 passing through the origin.".
- Real_projective_plane label "Plan projectif réel".
- Real_projective_plane label "Płaszczyzna rzutowa rzeczywista".
- Real_projective_plane label "Real projective plane".
- Real_projective_plane label "Reëel projectief vlak".
- Real_projective_plane label "实射影平面".
- Real_projective_plane sameAs Reálná_projektivní_rovina.
- Real_projective_plane sameAs Plan_projectif_réel.
- Real_projective_plane sameAs Reëel_projectief_vlak.
- Real_projective_plane sameAs Płaszczyzna_rzutowa_rzeczywista.
- Real_projective_plane sameAs m.0253h2.
- Real_projective_plane sameAs Q633815.
- Real_projective_plane sameAs Q633815.
- Real_projective_plane sameAs Real_projective_plane.
- Real_projective_plane wasDerivedFrom Real_projective_plane?oldid=590056131.
- Real_projective_plane depiction ProjectivePlaneAsSquare.svg.
- Real_projective_plane isPrimaryTopicOf Real_projective_plane.
