All articles starting with G
18,970 articles
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 morphometrics
Geometric morphometrics is the statistical analysis of biological form based on landmark coordinates, separating shape from size, position, and orientation; it is widely used in evolutionary biology and aquaculture.
Geometric phase
The geometric phase, also called the Berry phase, is a phase acquired by a quantum system over cyclic evolution that depends on the path's geometry, not its duration.
Geometric phase analysis
Geometric phase analysis is a Fourier-domain method for measuring strain fields from high-resolution electron microscope images, developed by Martin J. Hÿtch and colleagues in 1998.
Geometric phase metasurface
A geometric phase metasurface, or Pancharatnam–Berry (PB) metasurface, is an ultrathin optical device whose rotated anisotropic nanostructures give converted light a phase of twice the local rotation angle, dispersion-free in origin.
Geometric programming
Geometric programming is an optimization method with posynomial objectives and constraints that becomes convex after a logarithmic change of variables, so interior-point algorithms find the global optimum efficiently.
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.
Geometric Tools
Geometric Tools is a collection of freely downloadable C++ source code for mathematics, geometry, graphics, image analysis, and physics, maintained by David Eberly and distributed under the Boost License.
Geometrical optics
Geometrical optics, also called geometric or ray optics, is the branch of optics that models light as straight-line rays, valid when objects are much larger than the wavelength.
Geometrically exact beam formulation
The geometrically exact beam formulation, known as Cosserat rod theory or GEBT, is a structural model that represents arbitrarily large beam displacements and rotations exactly, used in soft robotics.
Geometridae
Geometridae, geometer moths, a species-rich Lepidoptera family of nearly 24,000 species in nine subfamilies; larvae are inchworms with two or three proleg pairs, worldwide except Antarctica.
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.
Geometrized unit system
The geometrized unit system, also called geometric units, sets the gravitational constant and the speed of light to 1, so mass, length, and time share one unit.
Geometrodynamics
Geometrodynamics is a research program in general relativity treating gravity as the dynamics of spacetime geometry itself; John Wheeler coined the term in 1962 by analogy with electrodynamics.
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 Dash
Geometry Dash: rhythm-based action platformer by RobTop Games (Robert Topala), iOS 2013, Steam 2014; one-touch, no checkpoints, level editor, rating system, Update 2.2 after seven years.
Geometry Engine (SGI)
The Geometry Engine was a VLSI floating-point chip for 3D graphics, developed by James H. Clark at Stanford and commercialized by Silicon Graphics as the core of its IRIS workstations.
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.
Geometry Partners (上海几何伙伴智能驾驶有限公司) (几何伙伴)
Geometry Partners (上海几何伙伴智能驾驶有限公司) is a Shanghai autonomous-driving startup founded in October 2018 by Xue Dan, developing 4D millimeter-wave imaging radar and L2–L4 fusion perception systems, with SAIC as its anchor customer.