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...

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...

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

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}...

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...

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,...

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...

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

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

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

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

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

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

with the above definition since in the unique projective extension of the affine plane to a projective plane a single point (point at infinity) is added...

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...

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...

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

geometry, since the common construction of the real projective plane is as the space of lines in R3 passing through the origin. The real projective plane...

are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the...

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...

and more specifically in projective geometry, a projective frame or projective basis is a tuple of points in a projective space that can be used for...

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...

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...

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

points of projective space. A notable property of the projective elliptic geometry is that for even dimensions, such as the plane, the geometry is non-orientable...