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

considered to change under projective transformations. The name projective comes from perspective drawing: projecting an image from one plane onto another as viewed...

coordinates in the traditional sense of projective geometry. The Betti numbers of the complex projective plane are 1, 0, 1, 0, 1, 0, 0, ..... The middle...

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...

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

concept of plane duality readily extends to space duality and beyond that to duality in any finite-dimensional projective geometry. A projective plane C may...

standard notation for this plane, as a member of a family of projective spaces, is PG(2, 2). Here, PG stands for "projective geometry", the first parameter...

In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that...

In projective geometry an oval is a point set in a plane that is defined by incidence properties. The standard examples are the nondegenerate conics....

Cayley plane, lines and points may be defined in a natural way so that it becomes a 2-dimensional projective space, that is, a projective plane. It is...

smooth projective planes are special projective planes. The most prominent example of a smooth projective plane is the real projective plane E {\displaystyle...

algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous...

Rosenfeld projective planes and notated as if they were projective planes. More broadly, these compact forms are the Rosenfeld elliptic projective planes, while...

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 (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations...

the projective planes, there are also seven lines; each point is on three lines, and each line contains three points. This particular projective plane is...

In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases...

a projective plane. Since a projective plane is a self-dual configuration, the dual configuration of an affine plane is obtained from a projective plane...

} . A projective mapping is a finite sequence of perspective mappings. As a projective mapping in a projective plane over a field (pappian plane) is uniquely...

fake projective plane (or Mumford surface) is one of the 50 complex algebraic surfaces that have the same Betti numbers as the projective plane, but are...

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...

a Desarguesian plane. The theorem of Desargues is true in all projective spaces of dimension not 2; in other words, the only projective spaces of dimension...

referred to as arcs in the literature, is the (k, d)-arcs. In a finite projective plane π (not necessarily Desarguesian) a set A of k (k ≥ 3) points such that...

In projective geometry and mathematics more generally, a projective line is, roughly speaking, the extension of a usual line by a point called a point...

dimension of the projective space being considered. For example, two homogeneous coordinates are required to specify a point on the projective line and three...

In geometry, Boy's surface is an immersion of the real projective plane in three-dimensional space. It was discovered in 1901 by the German mathematician...

affine plane obtained by removing l from the plane Π. A projective plane with a translation line is called a translation plane and the affine plane obtained...

a finite projective plane of order n has n+1 points on each line, and n2+n+1 points and lines. This implies that a finite projective plane of order n−1...

In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates...

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...