6,052 articles
Vertex-transitive graph
A vertex-transitive graph, also called point-symmetric or node-symmetric, is a graph whose symmetries can map any vertex to any other, so it looks the same from every vertex.
Vertical and horizontal
Vertical and horizontal are the two reference directions of space: a vertical line runs up and down along gravity, and a horizontal line runs straight across.
Vertical bar
The vertical bar, also called the pipe, is a glyph, encoded as U+007C, that serves as a punctuation mark, a mathematical symbol, and a heavily used character in computing.
Vesica piscis
The vesica piscis is the lens-shaped figure formed by two equal circles whose centers lie on each other's circumference, used in Gothic architecture and Christian art.
Victor Klee
Victor Klee (1925–2007) was an American mathematician at the University of Washington, called the father of the modern theory of convex polytopes, who posed the art gallery problem.
Video tracking
Video tracking is the computer vision task of following one or more moving objects across a sequence of video frames, given an initial location such as a bounding box.
Vieta jumping
Vieta jumping, also called root flipping, is a number theory proof technique for symmetric quadratic Diophantine equations, famous from Problem 6 of the 1988 International Mathematical Olympiad.
Vieta's formulas
Vieta's formulas relate a polynomial's coefficients to the sums and products of its roots; for ax² + bx + c, the roots add to −b/a and multiply to c/a.
Vigenère cipher
The Vigenère cipher, called le chiffre indéchiffrable, is a polyalphabetic substitution cipher using a repeating keyword, considered unbreakable for about 300 years until Kasiski's 1863 attack.
VIKOR method
The VIKOR method is a multi-criteria decision-making method that ranks alternatives by their distance from ideal and anti-ideal solutions, returning a compromise solution or compromise set.
Vinculum (symbol)
A vinculum is a horizontal bar over mathematical symbols showing they form one unit, first used in 1484 and familiar today in repeating decimals and radical signs.
Vine copula
A vine copula is a statistical model for dependence among several random variables, built from bivariate copulas arranged in a graphical structure called a regular vine.
Vinogradov's mean value theorem
Vinogradov's mean value theorem is a theorem in analytic number theory giving the correct order of magnitude for Vinogradov's integral, proved by Wooley and by Bourgain, Demeter, and Guth.
Virasoro algebra
The Virasoro algebra is an infinite-dimensional Lie algebra, the universal central extension of the Witt algebra of vector fields, and the algebraic home of two-dimensional conformal symmetry in conformal field theory and string theory.
Virtual element method
The virtual element method (VEM) is a numerical method for solving partial differential equations on meshes of arbitrary polygons or polyhedra, extending finite element ideas to shapes standard finite elements cannot handle.
Virtual Haken conjecture
The virtual Haken conjecture states that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken; it was conjectured by Waldhausen and proved by Ian Agol in 2012.
Viscosity solution
A viscosity solution is a generalized solution of a nonlinear partial differential equation, introduced by Crandall and Lions in 1983 for equations with no classical solution.
Viscous Hamilton–Jacobi equation
The viscous Hamilton–Jacobi equation is a Hamilton–Jacobi equation with a diffusion term added, so solutions are smoother and converge, as viscosity vanishes, to the viscosity solution of the inviscid equation.
Visibility graph
A visibility graph is a graph whose edges join pairs of points or polygon vertices that can see each other, used in robotics for shortest-path planning around obstacles.
Voevodsky motives
Voevodsky motives are objects of triangulated categories of motives over a field, constructed by Vladimir Voevodsky as a candidate for the hypothetical category of mixed motives.
Vojta's conjecture
Vojta's conjecture is a predicted height inequality in Diophantine geometry formulated by Paul Vojta in 1987; it generalizes Roth's and Faltings' theorems and relates to the abc conjecture.
Volterra integral equation
A Volterra integral equation is an integral equation in which the integral's upper limit is the independent variable x, making it always uniquely solvable and equivalent to initial value problems.
Volterra series
The Volterra series is a functional expansion representing the output of nonlinear systems with memory as multi-dimensional convolutions, often described as a Taylor series with memory.
Volume
Volume is the measure of the three-dimensional space occupied by matter or enclosed by a surface, expressed in cubic units; the SI unit is the cubic meter.
Volume form
A volume form is a nowhere-zero differential n-form on a smooth manifold, equivalently a nowhere-vanishing section of the top exterior power of its cotangent bundle.
Von Mangoldt function
The von Mangoldt function Λ(n) is an arithmetic function in analytic number theory, equal to log p when n is a power of a prime p and 0 otherwise.
Von Neumann algebra
A von Neumann algebra, also called a W-algebra, is a weakly closed self-adjoint algebra of bounded operators on a Hilbert space, introduced by John von Neumann in 1929.
Von Neumann universal constructor
The Von Neumann universal constructor, also called the Von Neumann replicator, is a theoretical machine conceived by John von Neumann in the late 1940s that can build any machine.
Von Neumann universe
The von Neumann universe, or cumulative hierarchy, is the class V of all well-founded sets, built from the empty set in transfinite stages indexed by the ordinals.
Von Neumann–Bernays–Gödel set theory
Von Neumann–Bernays–Gödel set theory (NBG) is a finitely axiomatizable axiomatic set theory whose objects are classes; it proves exactly the same statements about sets as ZFC.