Physical world and mathematics

Projectile motion

Projectile motion, also called ballistic trajectory, is the motion of an object thrown into the air under gravity alone; in the idealized model its path is a parabola.

Projection (linear algebra)

A projection in linear algebra is an idempotent linear operator, meaning applying it twice gives the same result as once, sending every vector to a chosen subspace.

Projection lattice and comparison theory

The projection lattice of a von Neumann algebra is its complete lattice of projections, ordered by positivity, with Murray–von Neumann equivalence and comparison theory deciding when projections are equivalent.

Projection method (fluid dynamics)

The projection method is a time-stepping technique for the incompressible Navier–Stokes equations, introduced by Chorin and Témam in the late 1960s, that splits each step into an intermediate velocity solve and a pressure projection.

Projection pursuit

Projection pursuit is a statistical technique that searches one- and two-dimensional projections of high-dimensional data for the most interesting views, making clusters, holes, and nonlinearity visible.

Projection pursuit regression

Projection pursuit regression (PPR) is a nonparametric regression method introduced by Jerome Friedman and Werner Stuetzle in 1981, modeling a response as a sum of smooth functions of linear predictor combinations.

Oct 22, 2026

Projection-based embedding

Projection-based embedding is a quantum embedding method in electronic structure theory, introduced in 2012 by Frederick R. Manby and Thomas F. Miller III and co-workers.

Projective cover

A projective cover of a module M is a surjection from a projective module with superfluous kernel; unique when it exists, though not every module has one.

Projective dimension

Projective dimension is an invariant of a module over a ring, the minimum length of a projective resolution, measuring how far the module is from being projective.

Projective duality

Projective duality is a symmetry of projective geometry in which the roles of points and lines can be exchanged, so the dual of any true theorem is also true.

Projective geometry

Projective geometry is the branch of mathematics studying properties of figures that survive projection, keeping incidence and the cross-ratio while discarding distance, angle, and parallelism; it underlies perspective and computer vision.

Projective hierarchy

The projective hierarchy is a classification of sets of real numbers, built from the analytic sets by complementation and projection, introduced by Lusin and Sierpiński in 1925.

Projective Hilbert space

The projective Hilbert space is the space of quantum pure states, formed from a Hilbert space by identifying vectors that differ by a nonzero complex factor.

Projective line

The projective line is the one-dimensional projective space over a field K, formed by adding a single point at infinity to the ordinary affine line.

Projective measurement (quantum mechanics)

A projective measurement, also called a von Neumann measurement, is a quantum-mechanical measurement whose outcomes are the eigenvalues of the measured observable, to which the state is projected.

Projective module

A projective module, also called a finitely generated projective module in the finite case, is a module over a ring that behaves like a free module, characterized by the lifting property for homomorphisms.

Projective plane

A projective plane is a geometric structure of points and lines in which every pair of lines meets, achieved by adding points at infinity to parallel lines.

Projective representation

A projective representation of a group assigns operators to group elements that multiply only up to a scalar factor, classified by the second group cohomology H²(G, U(1)).

Projective resolution

A projective resolution of a module is an exact sequence of projective modules ending in it, the standard tool for computing derived functors such as Ext and Tor.

Projective space

Projective space, written KP^n, is the set of lines through the origin of a vector space, adding points at infinity so any two lines meet in one point.

Projective variety

A projective variety is a subset of projective space cut out by homogeneous polynomials, one of the two basic objects of classical algebraic geometry alongside affine varieties.

Projector

A projector, also called an image projector, is an optical instrument that casts an enlarged image from film, a transparency, or a display chip onto a screen.

Projector augmented-wave method

The projector augmented-wave (PAW) method is an electronic structure method for density functional theory, introduced by P. E. Blöchl in 1994, that combines pseudopotential efficiency with all-electron accuracy.

Prokhorov's theorem

Prokhorov's theorem is a result in probability theory stating that a family of probability measures on a Polish space is tight if and only if every sequence has a weakly convergent subsequence.

Proleptic Gregorian calendar

The proleptic Gregorian calendar is the Gregorian calendar extended backward before its 1582 introduction, applying today's leap-year rules to dates as if it had always existed.

Prolific (participant recruitment platform)

Prolific is an online platform founded in 2014 that connects academic researchers, AI developers, and product teams with a vetted pool of paid participants for surveys, experiments, and AI training data.

Proline

Proline (Pro) is the only proteinogenic secondary amino acid, with a pyrrolidine ring bonded to its backbone nitrogen; it stabilizes collagen's triple helix and runs a redox-linked P5C metabolic cycle.

Promax rotation

Promax rotation is a two-stage oblique factor rotation in exploratory factor analysis, proposed by Hendrickson and White in 1964 as a fast alternative to analytic methods.

Promazine

Promazine is a low-potency aliphatic phenothiazine antipsychotic, used clinically as the hydrochloride salt mainly for sedation and agitation, and the parent compound from which chlorpromazine was derived by chlorination in 1950.