projective line
English
editNoun
editprojective 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 one-dimensional subspaces in , the projective lines correspond to two-dimensional 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 so-called 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
editTranslations
editline with point at infinity
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See also
editFurther 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