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Topics referred to by the same term
Look up projective in Wiktionary, the free dictionary. Projective may refer to Projective geometry Projective space Projective plane Projective variety
Projective
Type of geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that
Projective_geometry
Geometric concept of a 2D space with "points at infinity" adjoined
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
Projective_plane
Completion of the usual space with "points at infinity"
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
Projective_space
Psychological defense mechanism
Projective identification is a term introduced by Melanie Klein and then widely adopted in psychoanalytic psychotherapy. Projective identification may
Projective_identification
Algebraic variety in a projective space
In algebraic geometry, a projective variety is an algebraic variety that is a closed subvariety of a projective space. That is, it is the zero-locus in
Projective_variety
Type of personality test
In psychology, a projective test is a personality test designed to let a person respond to ambiguous stimuli, presumably revealing hidden emotions and
Projective_test
Direct summand of a free module (mathematics)
the property of lifting that carries over from free to projective modules: a module P is projective if and only if for every surjective module homomorphism
Projective_module
Construction in group theory
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
Projective_linear_group
Fiber bundle whose fibers are projective spaces
In mathematics, a projective bundle is a fiber bundle whose fibers are projective spaces. By definition, a scheme X over a Noetherian scheme S is a Pn-bundle
Projective_bundle
Compact non-orientable two-dimensional manifold
real projective plane, denoted R P 2 {\displaystyle \mathbf {RP} ^{2}} or P 2 {\displaystyle \mathbb {P} _{2}} , is a two-dimensional projective space
Real_projective_plane
Isomorphism of projective spaces in geometry
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces
Homography
mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets. The axiom of projective determinacy
Projective_determinacy
Line with a point at infinity added
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
Projective_line
Map from algebra to geometric transforms
mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group P
Projective_representation
Type of object in category theory
In category theory, the notion of a projective object generalizes the notion of a projective module. Projective objects in abelian categories are used
Projective_object
Supersymmetric-theory-dealing way in supersymmetry and quantum physics
In supersymmetry, a theory of particle physics, projective superspace is one way of dealing with N = 2 {\displaystyle {\mathcal {N}}=2} supersymmetric
Projective_superspace
Branch of mathematics
form only in projective space. For these reasons, projective space plays a fundamental role in algebraic geometry. Nowadays, the projective space Pn of
Algebraic_geometry
Mathematical object studied in the field of algebraic geometry
called a projective algebraic set if V = Z(S) for some S. An irreducible projective algebraic set is called a projective variety. Projective varieties
Algebraic_variety
category theory, a projective cover of an object M is in a sense the best approximation of M by a projective object P. Projective covers are the dual
Projective_cover
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
Ovoid_(projective_geometry)
Coordinate system used in projective geometry
dimension of the projective space being considered. For example, two homogeneous coordinates are required to specify a point on the projective line and three
Homogeneous_coordinates
quasi-projective variety in algebraic geometry is a locally closed subset of a projective variety, i.e., the intersection inside some projective space
Quasi-projective_variety
Concept in projective geometry
duality and beyond that to duality in any finite-dimensional projective geometry. A projective plane C may be defined axiomatically as an incidence structure
Duality_(projective_geometry)
Mathematical concept
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
Complex_projective_space
Quotient of special unitary group by its center
isometry group of complex projective space, just as the projective orthogonal group is the isometry group of real projective space. In terms of matrices
Projective_unitary_group
Curve from a cone intersecting a plane
{\displaystyle \pi } . A projective mapping is a finite sequence of perspective mappings. As a projective mapping in a projective plane over a field (pappian
Conic_section
Model of the extended complex plane plus a point at infinity
manifolds. In projective geometry, the sphere is an example of a complex projective space and can be thought of as the complex projective line P 1 ( C
Riemann_sphere
Type of transport in differential geometry
having the same unparametrized geodesics. Projective connections are modeled on the geometry of projective space. In modern terms, they may be described
Projective_connection
Type of topological space
standard round metric, the measure of projective space is exactly half the measure of the sphere. Real projective spaces are smooth manifolds. On Sn, in
Real_projective_space
Concept in mathematics
In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates
Quaternionic_projective_space
In projective geometry and linear algebra, the projective orthogonal group PO is the induced action of the orthogonal group of a quadratic space V = (V
Projective_orthogonal_group
Assignment planned to achieve a objective
Look up project in Wiktionary, the free dictionary. A project is a type of assignment, typically involving research or design, that is carefully planned
Project
In algebraic geometry, a weighted projective space P(a0,...,an) is the projective variety Proj(k[x0,...,xn]) associated to the graded ring k[x0,...,xn]
Weighted_projective_space
Exact sequence used to describe the structure of an object
resolutions, projective resolutions and flat resolutions, which are left resolutions consisting, respectively of free modules, projective modules or flat
Resolution_(algebra)
Geometry
the oldest part of the theory (for the projective line), namely the Schwarzian derivative, the simplest projective differential invariant. Further work
Projective differential geometry
Projective_differential_geometry
Point found separated from another, given a point pair
In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following
Projective_harmonic_conjugate
Manifold or algebraic variety of dimension n in a space of dimension n+1
a projective hypersurface, called its projective completion, whose equation is obtained by homogenizing p. That is, the equation of the projective completion
Hypersurface
Plane tiling corresponding to a polyhedron
In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations
Projective_polyhedron
Attributing parts of the self to others
Freud, projective identification occurs when the other person introjects, or unconsciously adopts, that which is projected onto them. In projective identification
Psychological_projection
Algebra where division is always defined
produces a projective line extended to a wheel by adjoining a bottom element noted ⊥, where 0 / 0 = ⊥ {\displaystyle 0/0=\bot } . The projective line is
Wheel_theory
2D surface which extends indefinitely
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
Plane_(mathematics)
Mathematical card game
among them. The word projective comes from the game's relation to projective spaces over the finite field with two elements. Projective Set has been studied
Projective_Set_(game)
In projective geometry, points that define coordinates
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
Projective_frame
Generalized Euclidean space in mathematics
v ] {\displaystyle [v]} are also referred to as rays or projective rays. Each such projective ray is a copy of the nonzero complex numbers, which is topologically
Projective_Hilbert_space
Descriptive set theory concept
is projective iff it is definable in the language of second-order arithmetic from some real parameter. A similar relationship between the projective hierarchy
Projective_hierarchy
Projective line over the real numbers
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
Real_projective_line
finite projective plane of even order. A k-arc which can not be extended to a larger arc is called a complete arc. In the Desarguesian projective planes
Arc_(projective_geometry)
Set of points in a projective line or conic
mathematics, a projective range is a set of points in projective geometry considered in a unified fashion. A projective range may be a projective line or a
Projective_range
Subspace of n-space whose dimension is (n-1)
the solution of a single linear equation. Projective hyperplanes are used in projective geometry. A projective subspace is a set of points with the property
Hyperplane
Conservative political initiative in the United States
Project 2025 (also known as the 2025 Presidential Transition Project) is a political initiative published in April 2023 by the Heritage Foundation with
Project_2025
a 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
Fake_projective_plane
World War II Allied nuclear weapons program
The Manhattan Project was a research and development program undertaken during World War II to produce the first nuclear weapons. It was led by the United
Manhattan_Project
Curve defined as zeros of polynomials
zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three
Algebraic_curve
Well studied projective geometries over finite fields
planes. In projective geometry, a specific instance of this problem that has numerous applications is determining whether, and how, a projective space can
Spread_(projective_geometry)
Locus of the zeros of a polynomial of degree two
affine algebraic set. Quadrics may also be defined in projective spaces; see § Normal form of projective quadrics, below. In coordinates x1, x2, ..., xD+1
Quadric
Relation between Lie algebras depicted as a square
the octonionic projective plane – FII, dimension 16 = 2 × 8, F4 symmetry, Cayley projective plane P2(O), the bioctonionic projective plane – EIII, dimension
Freudenthal_magic_square
Family of geometric objects with a common property
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
Pencil_(geometry)
Concept in geometry
dimensions, all the points at infinity form a projective subspace of one dimension less than that of the whole projective space to which they belong. A point at
Point_at_infinity
Projective plane
In mathematics, the Cayley plane (or octonionic projective plane) P2(O) is a projective plane over the octonions. The Cayley plane was discovered in 1933
Cayley_plane
Geometric shape
Linnaeus Wayland (1917-01-01). Projective Geometry. McGraw-Hill book Company, Incorporated. G. B. Halsted (1906) Synthetic Projective Geometry, page 20 Protter
Cone
Complex algebraic variety
In mathematics, a fake projective space is a complex algebraic variety that has the same Betti numbers as some projective space, but is not isomorphic
Fake_projective_space
2021 science-fiction novel by Andy Weir
Project Hail Mary is a 2021 hard science fiction novel by American writer Andy Weir. It centers on science teacher and former biologist Ryland Grace,
Project_Hail_Mary
fundamental geometric statement on projective spaces: the Euler sequence. The negativity of the canonical line bundle makes projective spaces prime examples of
Algebraic geometry of projective spaces
Algebraic_geometry_of_projective_spaces
A projective cone (or just cone) in projective geometry is the union of all lines that intersect a projective subspace R (the apex of the cone) and an
Projective_cone
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
Truncated_projective_plane
Oriented projective geometry is an oriented version of real projective geometry. Whereas the real projective plane describes the set of all unoriented
Oriented_projective_geometry
Geometric system with a finite number of points
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
Finite_geometry
Invariant in projective geometry
is essentially the only projective invariant of a quadruple of collinear points; this underlies its importance for projective geometry. The cross-ratio
Cross-ratio
2-dimensional complex projective space
homogeneous 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
Complex_projective_plane
abstract algebra, Kaplansky's theorem on projective modules, first proven by Irving Kaplansky, states that a projective module over a local ring is free; where
Kaplansky's theorem on projective modules
Kaplansky's_theorem_on_projective_modules
commutative ring assigned to any projective variety. If V is an algebraic variety given as a subvariety of projective space of a given dimension N, its
Homogeneous_coordinate_ring
Number used in algebraic geometry
In mathematics, the degree of an affine or projective variety of dimension n is the number of intersection points of the variety with n hyperplanes in
Degree of an algebraic variety
Degree_of_an_algebraic_variety
Circle-like pointset in a geometric plane
a projective space. A generalization of the oval concept is an abstract oval, which is a structure that is not necessarily embedded in a projective plane
Oval_(projective_plane)
Projective construction in ring theory
mathematics, the projective line over a ring is an extension of the concept of projective line over a field. Given a ring A (with 1), the projective line P1(A)
Projective_line_over_a_ring
map induces a projectivity. The converse of this observation (except for the projective line) is the fundamental theorem of projective geometry. Thus
Semilinear_map
Projective analogue of the spectrum of a ring
schemes, which produces objects with the typical properties of projective spaces and projective varieties. The construction, while not functorial, is a fundamental
Proj_construction
projector. Projective texture mapping is useful in a variety of lighting techniques and it is the starting point for shadow mapping. Projective texture mapping
Projective_texture_mapping
Theorem about orthocenter and polars in circle geometry
(also known as Brocard's theorem) is a theorem on poles and polars in projective geometry commonly used in Olympiad mathematics. It is named after French
Brokard's_theorem
Branch of finite geometry
a Galois geometry may be defined as a projective space over a finite field. Objects of study include affine and projective spaces over finite fields and various
Galois_geometry
Shape
egg. The term is not very specific, but in some areas of mathematics (projective geometry, technical drawing, etc.), it is given a more precise definition
Oval
Topics referred to by the same term
Look up projection, projecting, projective, or projector in Wiktionary, the free dictionary. Projection or projections may refer to: Projection (physics)
Projection
Map in projective geometry
embedding is a map used in projective geometry to consider the cartesian product of two projective spaces as a projective variety. It is named after Corrado
Segre_embedding
Concept in projective geometry
In projective geometry, a correlation is a transformation of a d-dimensional projective space that maps subspaces of dimension k to subspaces of dimension
Correlation (projective geometry)
Correlation_(projective_geometry)
Projective plane not satisfying Desargues' theorem
in all projective spaces of dimension not 2; in other words, the only projective spaces of dimension not equal to 2 are the classical projective geometries
Non-Desarguesian_plane
Self-intersecting compact surface, an immersion of the real projective plane
of the real projective plane, RP2 by a smooth map. That is, the parametrization of the Boy's surface is an immersion of the real projective plane into
Boy's_surface
American charitable organization
websites in the world. It also hosts fourteen related open collaboration projects, and supports the development of MediaWiki, the wiki software which underpins
Wikimedia_Foundation
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
equal to 1 is simple for all odd n > 1, when it is isomorphic to the projective special linear group. The first classification of simple Lie groups was
Simple_Lie_group
UFO conspiracy theory
06222; -71.87389 The Montauk Project is a conspiracy theory that alleges there were a series of United States government projects conducted at Camp Hero or
Montauk_Project
Nonexistence result for combinatorial block designs
a projective plane, the theorem (which in this case is referred to as the Bruck–Ryser theorem) can be stated as follows: If a finite projective plane
Bruck–Ryser–Chowla_theorem
Type of mathematical space
generalized flag variety is defined to mean a projective homogeneous variety, that is, a smooth projective variety X over a field F with a transitive action
Generalized_flag_variety
Type of algebraic variety
is projective, there exist nonsingular complete varieties in dimension 3 and higher which are not projective. The first examples of non-projective complete
Complete_variety
Moduli scheme of subschemes of a scheme, represents the flat-family-of-subschemes functor
of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes
Hilbert_scheme
Field of algebraic geometry
birational to a projective variety (Chow's lemma). So, for the purposes of birational classification, it is enough to work only with projective varieties,
Birational_geometry
Rational surface in 5-dimensional projective space
surface in five-dimensional projective space, and is realized by the Veronese embedding, the embedding of the projective plane given by the complete linear
Veronese_surface
Topics referred to by the same term
Project A may refer to: Project A (film), 1983 martial arts action-comedy film Project A Part II, 1987 Hong Kong martial arts action-comedy film Project
Project_A
geometry, smooth projective planes are special projective planes. The most prominent example of a smooth projective plane is the real projective plane E {\displaystyle
Smooth_projective_plane
{\displaystyle Y} gives a norm, called the projective norm, on X ⊗ Y {\displaystyle X\otimes Y} which generates the projective topology. Throughout, all spaces
Projective_tensor_product
Algebraic structure in ring theory
projective, or torsion-free. In particular, every flat module is torsion-free, every projective module is flat, and every free module is projective.
Flat_module
Type of mathematical curve
projective space of dimension three over the field of the complex numbers (or over an algebraic closure of k {\displaystyle k} ), whose projective
Cubic_plane_curve
PROJECTIVE
PROJECTIVE
PROJECTIVE
PROJECTIVE
Male
Danish
, Christian, follower of Christ.
Male
Russian
(Илларион) Russian form of Greek Hilarion, ILLARION means "joyful; happy."
Male
Russian
(Колода) Russian name KOLODA means "log."
Boy/Male
Muslim
Power. Dignity.
Girl/Female
Arabic, Islamic, Muslim, Pakistani, Urdu
Simple; Exotic; Noble; Princess
Girl/Female
African, Australian, Hebrew
A Dancer; From Bobangi; Knowledge; Perception
Girl/Female
Indian
Love
Girl/Female
Indian, Telugu
Good Eyes
Female
Polish
Polish form of Greek Iolanthe, JOLANTA means "violet flower."
Girl/Female
Hindu, Indian
Mountain
PROJECTIVE
PROJECTIVE
PROJECTIVE
PROJECTIVE
PROJECTIVE