projective line
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English[edit]
Noun[edit]
projective line (plural projective lines)
 (projective geometry) A line that includes a point at infinity; a line in a projective space; a projective space of dimension 1.
 2007, Unnamed translator, Ana Irene Ramírez Galarza, José Seade, Introduction to Classical Geometries, [2002, Introducciòn a la Geometria Avanzada], Springer (Birkhäuser), page 97,
 In , the projective lines are defined by two projective points, that is, by two linearly independent directions of ; if we take one vector for each direction, the two vectors generate a plane through the origin in , that is, a subspace of dimension 2, and a projective line can be defined as follows:
 A projective line in , consists of the projective points defined by coplanar directions in .
 In other words, just as the points in correspond to onedimensional subspaces in , the projective lines correspond to twodimensional subspaces in .
 2008, Catriona Maclean (translator), Daniel Perrin, Algebraic Geometry: An Introduction, [1995, D. Perrin, Géométrie algébrique] Springer, page 37,
 Consider the projective line , with homogeneous coordinates and and open sets and .
 2009, Dirk Kussin, Noncommutative Curves of Genus Zero: Related to Finite Dimensional Algebras, American Mathematical Society, page 13,
 The projective line is related to the Kronecker algebra, […] In general one has to deal with the socalled weighted case which leads to the study of the canonical algebras and to the weighted projective lines (as Ringel pointed out in his survey [93]).
 2007, Unnamed translator, Ana Irene Ramírez Galarza, José Seade, Introduction to Classical Geometries, [2002, Introducciòn a la Geometria Avanzada], Springer (Birkhäuser), page 97,
Synonyms[edit]
 (line with a point at infinity): projective straight line
Derived terms[edit]
Translations[edit]
line with point at infinity

See also[edit]
Further reading[edit]
 Point at infinity on Wikipedia.Wikipedia
 Projective geometry on Wikipedia.Wikipedia
 Projective plane on Wikipedia.Wikipedia
 Projective space on Wikipedia.Wikipedia
 Projection (mathematics) on Wikipedia.Wikipedia
 Graphical projection on Wikipedia.Wikipedia
 Perspective (graphical) on Wikipedia.Wikipedia
 Vanishing point on Wikipedia.Wikipedia
 Projective straight line on Encyclopedia of Mathematics
 Point at Infinity on Wolfram MathWorld
 Projective lines on nLab