Projection, projections or projective may refer to:

Physics

Projection (physics) The vector projection of a vector on (or onto) a nonzero vector , sometimes denoted \operatorname_\mathbf \mathbf (also known as the vector component or vector resolution of in the direction of ), is the orthogonal projection of onto a straig ...

, the action/process of light, heat, or sound reflecting from a surface to another in a different direction * The display of images by a

projector A projector or image projector is an optical device that projects an image (or moving images) onto a surface, commonly a projection screen. Most projectors create an image by shining a light through a small transparent lens, but some newer types ...

Optics, graphics, and cartography

Map projection In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitud ...

, reducing the surface of a three-dimensional planet to a flat map *

Graphical projection A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object fo ...

, the production of a two-dimensional image of a three-dimensional object

Chemistry

Fischer projection In chemistry, the Fischer projection, devised by Emil Fischer in 1891, is a two-dimensional representation of a three-dimensional organic molecule by projection. Fischer projections were originally proposed for the depiction of carbohydrates an ...

, a two-dimensional representation of a three-dimensional organic molecule *

Haworth projection In chemistry, a Haworth projection is a common way of writing a structural formula to represent the cyclic structure of monosaccharides with a simple three-dimensional perspective. Haworth projection approximate the shapes of the actual mole ...

, a way of writing a structural formula to represent the cyclic structure of monosaccharides *

Natta projection In chemistry, the Natta projection (named for Italian chemist Giulio Natta) is a way to depict molecules with complete stereochemistry in two dimensions in a skeletal formula. In a hydrocarbon molecule with all carbon atoms making up the backb ...

, a way to depict molecules with complete stereochemistry in two dimensions in a skeletal formula *

Newman projection A Newman projection is a drawing that helps visualize the 3-dimensional structure of a molecule. This projection most commonly sights down a carbon-carbon bond, making it a very useful way to visualize the stereochemistry of alkanes. A Newman pro ...

, a visual representation of a chemical bond from front to back

Mathematics

Projection (mathematics) In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition, i.e., which is idempotent. The restriction to a subspace of a project ...

, any of several different types of geometrical mappings **

Projection (linear algebra) In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself (an endomorphism) such that P\circ P=P. That is, whenever P is applied twice to any vector, it gives the same result as if it wer ...

, a linear transformation from a vector space to itself such that **

Projection (set theory) In set theory, a projection is one of two closely related types of functions or operations, namely: * A set-theoretic operation typified by the ''j''th projection map, written \mathrm_, that takes an element \vec = (x_1,\ \ldots,\ x_j,\ \ldots,\ x_ ...

, one of two closely related types of functions or operations in set theory ** Projection (measure theory), use of a projection map in measure theory **

3D projection A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object fo ...

, any method of mapping three-dimensional points to a two-dimensional plane **

Vector projection The vector projection of a vector on (or onto) a nonzero vector , sometimes denoted \operatorname_\mathbf \mathbf (also known as the vector component or vector resolution of in the direction of ), is the orthogonal projection of onto a straig ...

, orthogonal projection of a vector onto a straight line **

Projection (relational algebra) In relational algebra, a projection is a unary operation written as \Pi_( R ), where R is a relation and a_1,...,a_n are attribute names. Its result is defined as the set obtained when the components of the tuples in R are restricted to the set \ � ...

, a type of unary operation in relational algebra *

Projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pro ...

, the study of geometric properties that are invariant with respect to projective transformations *

Projective module In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules. Various equivalent characterizati ...

, a generalization of a free module *

Projective object In category theory, the notion of a projective object generalizes the notion of a projective module. Projective objects in abelian categories are used in homological algebra. The dual notion of a projective object is that of an injective object. ...

, a further generalization, in category theory *

Projection method (fluid dynamics) In fluid dynamics, The projection method is an effective means of numerically solving time-dependent incompressible fluid-flow problems. It was originally introduced by Alexandre Chorin in 1967 as an efficient means of solving the incompressible ...

, means of numerically solving time-dependent incompressible fluid-flow problems

Biology

Projection areas Projection areas are areas in the four lobes (frontal, parietal, temporal, occipital) of the brain A brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is ...

, areas of the brain where sensory processing occurs *

Projection fiber The projection fibers consist of efferent and afferent fibers uniting the cortex with the lower parts of the brain and with the spinal cord. In human neuroanatomy, bundles of axons (nerve fibers) called tracts, within the brain, can be catego ...

, in neuroscience, white matter fibers that connect the cortex to the lower parts of the brain or the spinal cord

Linguistics

Projection (linguistics) In linguistics, X-bar theory is a model of phrase-structure grammar and a theory of syntactic category formation that was first proposed by Noam Chomsky in 1970Chomsky, Noam (1970). Remarks on Nominalization. In: R. Jacobs and P. Rosenbaum (eds.) ...

, grammatical trait inheritance from a head to a phrasal category *

Projection principle In linguistics, the projection principle is a stipulation proposed by Noam Chomsky as part of the phrase structure component of generative-transformational grammar. The projection principle is used in the derivation of phrases under the auspices ...

in syntax * Projection of

presupposition In the branch of linguistics known as pragmatics, a presupposition (or PSP) is an implicit assumption about the world or background belief relating to an utterance whose truth is taken for granted in discourse. Examples of presuppositions include ...

s in linguistics

Arts and entertainment

* "Projections" (''Star Trek: Voyager''), an episode of the television series ''Star Trek: Voyager'' * ''Projections'' (The Blues Project album), 1966 * ''Projections'' (John Handy album), 1968 * ''Projections'' (film), 2013 Croatian film

Other uses

Projection (alchemy) Projection was the ultimate goal of Western alchemy. Once the philosopher's stone or powder of projection had been created, the process of projection would be used to transmute a lesser substance into a higher form; often lead into gold. Typ ...

, process in Alchemy * ''Projections'' (journal), an interdisciplinary academic journal related to cinema and visual media * Power projection, the capacity of a state to implement policy by means of force, or the threat thereof *

Psychological projection Psychological projection is the process of misinterpreting what is "inside" as coming from "outside". It forms the basis of empathy by the projection of personal experiences to understand someone else's subjective world. In its malignant forms, i ...

, or "Freudian projection", a defense mechanism in which one attributes to others one's own unacceptable or unwanted attributes, thoughts, or emotions *

Social projection In social psychology, social projection is the psychological process through which an individual expects behaviors or attitudes of others to be similar to their own. Social projection occurs between individuals as well as across ingroup and outgr ...

, a cognitive bias that leads people to believe others are similar to themselves *

Forecasting Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual ...

, making predictions of the future based on past and present data