projective line

Noun

 * 1)  A line that includes a point at infinity; a line in a projective space; a projective space of dimension 1.
 * 2) * 2007, Unnamed translator, Ana Irene Ramírez Galarza, José Seade, Introduction to Classical Geometries, [2002, Introducciòn a la Geometria Avanzada], Springer (Birkhäuser), page 97,
 * In $$P2(\R)$$, the projective lines are defined by two projective points, that is, by two linearly independent directions of $$\R^3$$; if we take one vector for each direction, the two vectors generate a plane through the origin in $$\R^3$$, that is, a subspace of dimension 2, and a projective line can be defined as follows:
 * A projective line in $$P^2(\R)$$, consists of the projective points defined by coplanar directions in $$\R^3$$.
 * In other words, just as the points in $$P^2(\R)$$ correspond to one-dimensional subspaces in $$\R^3$$, the projective lines correspond to two-dimensional subspaces in $$\R^3$$.
 * 1) * 2008, Catriona Maclean (translator), Daniel Perrin, Algebraic Geometry: An Introduction, [1995, D. Perrin, Géométrie algébrique] Springer, page 37,
 * Consider the projective line $$\mathbf{P}^1$$, with homogeneous coordinates $$x$$ and $$t$$ and open sets $$U_0\ (x \ne 0)$$ and $$U_1\ (t \ne 0)$$.

Translations

 * Italian: retta proiettiva