Projective Plane
A projective plane consists of a set of lines, a set of points, and a relation between points and lines called incidence, having the following properties:
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Some articles on projective plane:
Conic Section - Pencil of Conics
... by five points in general position (no three collinear) in a plane and the system of conics which pass through a fixed set of four points (again in a ... In a projective plane defined over an algebraically closed field any two conics meet in four points (counted with multiplicity) and so, determine the pencil of conics based on ... Let C1 and C2 be two distinct conics in a projective plane defined over an algebraically closed field K ...
... by five points in general position (no three collinear) in a plane and the system of conics which pass through a fixed set of four points (again in a ... In a projective plane defined over an algebraically closed field any two conics meet in four points (counted with multiplicity) and so, determine the pencil of conics based on ... Let C1 and C2 be two distinct conics in a projective plane defined over an algebraically closed field K ...
Examples - Extremal Length of Topologically Essential Paths in Projective Plane
... The projective plane with the spherical metric is obtained by identifying antipodal points on the unit sphere in with its Riemannian spherical metric ... Let denote the set of closed curves in this projective plane that are not null-homotopic ...
... The projective plane with the spherical metric is obtained by identifying antipodal points on the unit sphere in with its Riemannian spherical metric ... Let denote the set of closed curves in this projective plane that are not null-homotopic ...
Spherical Polyhedron - Relation To Tilings of The Projective Plane
... having at least one inversive symmetry are related to projective polyhedra (tessellations of the real projective plane) – just as the sphere has a 2-to-1 covering map of the ... For example, the 2-fold cover of the (projective) hemi-cube is the (spherical) cube ...
... having at least one inversive symmetry are related to projective polyhedra (tessellations of the real projective plane) – just as the sphere has a 2-to-1 covering map of the ... For example, the 2-fold cover of the (projective) hemi-cube is the (spherical) cube ...
Lift (mathematics)
... to the same point, a continuous map from the sphere covering the projective plane ... A path in the projective plane is a continuous map from the unit interval ... two starting points forces a unique path on the sphere, the lift of the path in the projective plane ...
... to the same point, a continuous map from the sphere covering the projective plane ... A path in the projective plane is a continuous map from the unit interval ... two starting points forces a unique path on the sphere, the lift of the path in the projective plane ...
Projective Planes in Higher Dimensional Projective Spaces
... Projective planes may be thought of as projective geometries of "geometric" dimension two ... Higher dimensional projective geometries can be defined in terms of incidence relations in a manner analogous to the definition of a projective plane ... These turn out to be "tamer" than the projective planes since the extra degrees of freedom permit Desargues' theorem to be proved geometrically in the higher ...
... Projective planes may be thought of as projective geometries of "geometric" dimension two ... Higher dimensional projective geometries can be defined in terms of incidence relations in a manner analogous to the definition of a projective plane ... These turn out to be "tamer" than the projective planes since the extra degrees of freedom permit Desargues' theorem to be proved geometrically in the higher ...
Famous quotes containing the word plane:
“We’ve got to figure these things a little bit different than most people. Y’know, there’s something about going out in a plane that beats any other way.... A guy that washes out at the controls of his own ship, well, he goes down doing the thing that he loved the best. It seems to me that that’s a very special way to die.”
—Dalton Trumbo (1905–1976)
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