respect to projective transformations, as is seen in perspective drawing from a changing perspective. One source for projective geometry was indeed the...

In projective geometry, duality or plane duality is a formalization of the striking symmetry of the roles played by points and lines in the definitions...

concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus...

the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can...

planar projective geometry, in which the relationships between objects are not considered to change under projective transformations. The name projective comes...

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces...

complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space...

theorems of geometry are simplified by the resultant elimination of special cases; for example, two distinct projective lines in a projective plane meet...

In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space P n {\displaystyle \mathbb {P}...

geometry, while it also develops the oldest part of the theory (for the projective line), namely the Schwarzian derivative, the simplest projective differential...

that are disregarded—projective geometry that consider only alignment of points but not distance and parallelism, affine geometry that omits the concept...

geometry that are related to symmetry. In traditional geometry, affine geometry is considered to be a study between Euclidean geometry and projective...

Galois geometries, since any finite projective space of dimension three or greater is isomorphic to a projective space over a finite field (that is, the...

algebraic geometry Noncommutative geometry Ordered geometry Parabolic geometry Plane geometry Projective geometry Quantum geometry Riemannian geometry Ruppeiner...

outline of an egg. The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition,...

absolute geometry, while negating it yields hyperbolic geometry. Other consistent axiom sets can yield other geometries, such as projective, elliptic...

form only in projective space. For these reasons, projective space plays a fundamental role in algebraic geometry. Nowadays, the projective space Pn of...

In geometry, a real projective line is a projective line over the real numbers. It is an extension of the usual concept of a line that has been historically...

Wayland (1917-01-01). Projective Geometry. McGraw-Hill book Company, Incorporated. G. B. Halsted (1906) Synthetic Projective Geometry, page 20 Protter, Murray...

In projective geometry an ovoid is a sphere like pointset (surface) in a projective space of dimension d ≥ 3. Simple examples in a real projective space...

statement is true in a projective plane, though not true in the Euclidean plane where lines may be parallel. Historically, projective geometry was developed in...

of a Projective space plays a central role in algebraic geometry. This article aims to define the notion in terms of abstract algebraic geometry and to...

of the 19th century, such as non-Euclidean, projective, and affine geometry. In the Greek deductive geometry of Euclid's Elements, a general line (now called...

especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action...

transformations; they all are projectively equivalent figures. The relation between the two geometries, Euclidean and projective,: 133  shows that mathematical...

In mathematics, the complex projective plane, usually denoted P2(C) or CP2, is the two-dimensional complex projective space. It is a complex manifold...

identified. RP1 is called the real projective line, which is topologically equivalent to a circle. RP2 is called the real projective plane. This space cannot be...

affine algebraic set. Quadrics may also be defined in projective spaces; see § Normal form of projective quadrics, below. As the dimension of a Euclidean plane...

particularly well-studied in projective geometries over finite fields, though some notable results apply to infinite projective geometries as well. In the finite...

the center of the directrix moves to the point at infinity (see Projective geometry). The directrix "circle" becomes a curve with zero curvature, indistinguishable...