6,052 articles
Geometric dimensioning and tolerancing
Geometric dimensioning and tolerancing (GD&T), also called geometric tolerancing, is a standardized symbolic language used on engineering drawings to define allowable variation in part geometry.
Geometric distribution
The geometric distribution is a discrete probability distribution modeling the number of independent trials until the first success, with fixed success probability p and mean 1/p.
Geometric graph theory
Geometric graph theory is the branch of graph theory that studies graphs drawn in the plane with straight-line or curved edges, focusing on crossings and extremal edge counts.
Geometric group theory
Geometric group theory studies groups as geometric objects through Cayley graphs and word metrics, drawing on topology and hyperbolic geometry; its modern form dates to Gromov's 1987 paper Hyperbolic groups.
Geometric invariant theory
Geometric invariant theory (GIT) is a framework in algebraic geometry introduced by David Mumford in 1965 for constructing quotients of algebraic varieties by group actions, notably moduli spaces.
Geometric Langlands program
The geometric Langlands program restates the Langlands correspondence as a statement in algebraic geometry, proved in 2024 by a team led by Dennis Gaitsgory and Sam Raskin.
Geometric lattice
A geometric lattice is a finite lattice in which every element is a join of atoms, equivalently the lattice of flats of a simple matroid.
Geometric logic
Geometric logic is a fragment of infinitary first-order logic allowing finite conjunctions, arbitrary set-indexed disjunctions, and existential quantification; it underlies the theory of classifying toposes.
Geometric mean
The geometric mean, also called the geometric average, is the n-th root of the product of n positive numbers, used for averaging growth rates and ratios.
Geometric progression
A geometric progression, also called a geometric sequence, is a sequence of numbers where each term is the previous term multiplied by a fixed common ratio.
Geometric quantization
Geometric quantization is a mathematical procedure that builds a quantum Hilbert space of states from a classical system whose phase space is a symplectic manifold, first reported by Souriau in 1966.
Geometric realization
Geometric realization is the functor converting a simplicial set into a topological space by gluing one standard geometric simplex for each abstract simplex, producing a CW complex with one cell per non-degenerate simplex.
Geometric series
A geometric series is an infinite series in which each term is a fixed multiple of the previous one, converging to a/(1−r) when the ratio's absolute value is below 1.
Geometrization conjecture
The geometrization conjecture of William Thurston, proved by Grigori Perelman via Ricci flow in 2002 and 2003, states that every compact 3-manifold cuts into pieces carrying one of eight geometries.
Geometry
Geometry, also called elementary geometry, is the branch of mathematics that studies spatial relationships and shapes, extended in modern times to non-Euclidean geometries used in Einstein's theory of relativity.
Geometry of interaction
The geometry of interaction is a semantic framework for linear logic, introduced by Jean-Yves Girard in the late 1980s, which models cut elimination by operators on Hilbert spaces rather than syntactic rewriting.
Geometry of numbers
The geometry of numbers, or geometric number theory, is a branch of number theory founded by Hermann Minkowski, studying how lattice points interact with convex bodies.
Georg Cantor
Georg Cantor, in full Georg Ferdinand Ludwig Philipp Cantor (1845–1918), was a German mathematician at the University of Halle who created set theory as a mathematical discipline.
George Boole
George Boole (1815–1864) was an English mathematician who reduced logic to an algebra; his Boolean logic, applied to circuits by Claude Shannon, underlies modern digital computing.
George Pólya Prize
The George Pólya Prize is a family of mathematics awards given by the Society for Industrial and Applied Mathematics, established in 1969 and named for George Pólya.
Georges Matheron
Georges Matheron (Georges François Paul Marie Matheron, 1930–2000) was a French mathematician and mining engineer who founded geostatistics, formalized kriging, and co-founded mathematical morphology with Jean Serra.
Gerhard Gentzen
Gerhard Gentzen (Gerhard Karl Erich Gentzen, 1909–1945) was a German mathematician and logician who created natural deduction and the sequent calculus, the two main logical calculi in proof theory.
German tank problem
The German tank problem is the statistical problem of estimating a population's size from observed serial numbers, used by the Allies in World War II.
Gerolamo Cardano
Gerolamo Cardano, also Girolamo Cardano, was an Italian physician, mathematician, and astrologer whose 1545 Ars Magna gave the first published solutions of cubic and quartic equations.
Gershgorin circle theorem
The Gershgorin circle theorem is a result in matrix analysis stating that every eigenvalue of a square matrix lies in disks centered at the diagonal entries, published in 1931.
GGE biplot analysis
GGE biplot analysis is a graphical statistical method for evaluating crop cultivars across environments, showing which genotype won where, mean performance, and stability, introduced by Weikai Yan and colleagues in 2000.
ggplot2
ggplot2 is an R package for declaratively creating statistical graphics based on the grammar of graphics, started by Hadley Wickham in 2005. It draws about 27.7 million CRAN downloads per year.
Giant component
A giant component is a connected subgraph of a random graph that contains a constant fraction of all vertices, its size growing in proportion to the graph itself.
Gibbs phenomenon
The Gibbs phenomenon, also called the Gibbs effect, is the fixed overshoot and undershoot of Fourier series partial sums near a jump discontinuity, persisting at about 8.95 percent of the jump.
Gibbs random field
A Gibbs random field is a random field whose probability is proportional to the exponential of a negative energy built from clique potentials, originating in statistical mechanics.