Mathematics

Unit circle The unit circle is the circle of radius 1 centered at the origin; it underpins trigonometric definitions, the Pythagorean identity, complex numbers on the unit modulus, and many ge…

Unit vector: definition, properties and common uses Unit vector A unit vector is a vector of length one. This article explains normalization, notation, properties, examples, computational concerns, and typical applications in science and engine…

Unitary Adjective and noun used in mathematics, physics, and political science: describes operators preserving inner products, groups of such matrices, and centralized state organization.

United States customary units Overview of the U.S. customary system: its principal length, area, volume, mass and temperature units, history of use and metrication, practical applications, and key differences f…

Universal quantifier (∀) Universal quantifier The universal quantifier (symbol ∀) expresses that a formula holds for every element of a domain. Overview, notation, semantics, proof rules, examples, and its relation to existenc…

Universe of discourse (domain of discourse) Universe of discourse The universe of discourse is the set of entities over which variables and quantifiers range in logic and mathematics; it clarifies meaning, scope and truth of formulas and queries.

Unknown (mathematics): variables, notation, history, and uses Unknown (math) Exposition of the mathematical concept of an unknown (variable), its notation, historical development, examples in algebra and physics, distinctions from constants and parameters,…

UNO: card game, numeral, and common acronyms UNO UNO — Spanish/Italian for 'one', the popular card game produced by Mattel, and an acronym used for organizations and products. Overview, gameplay elements, history, and other commo…

Validated numerics (reliable computation) Validated numerics Validated numerics is the practice of producing mathematically guaranteed bounds for numerical results, typically using interval arithmetic and related techniques to control and re…

Variable (mathematics, science, and computing) Variable An explanation of variables: their roles as placeholders for changeable or unknown values in mathematics, experiments, statistics, and programming, with types, examples, history, a…

Variance (probability and statistics) Variance Variance quantifies dispersion by averaging squared deviations from the mean. It is nonnegative, measured in squared units, and underpins standard deviation, risk measures and many…

Vector (mathematics and physics) Vector A vector is a mathematical object with magnitude and direction. Covers definitions, representations, operations (addition, dot and cross), history and common applications in scienc…

Vector calculus: concepts, operators, history and applications Vector calculus An overview of vector calculus: its core operators, historical development, mathematical context, and applications in physics and engineering.

Vector field (mathematics and physical interpretation) Vector field A vector field assigns a vector to each point of a space or manifold. Widely used in physics and engineering to represent velocity, force, and field quantities; studied via diverge…

Vector space A vector space is a set of objects called vectors closed under addition and scalar multiplication; it is the central structure of linear algebra with bases, dimension and many appl…

Venn diagram: graphical representation of relationships between sets Venn diagram A Venn diagram uses overlapping closed curves to show how sets relate—union, intersection, complement—and is widely used in mathematics, probability, logic, statistics and computer…

Vertex — corner point in geometry, polyhedra and graph theory Vertex A vertex is a point where two or more edges, lines or curves meet. Used in polygons, polyhedra, graphs and computer graphics; described by angle, valence (degree) and local geometr…

Vertex figure A vertex figure is the local polygon or polytope formed at a vertex of a polyhedron or polytope, obtained by slicing or intersecting near that vertex; used to study local geometry…

Vertical angles (vertically opposite angles) Vertical angles Vertical angles are the pair(s) of opposite, nonadjacent angles formed when two lines intersect; they are congruent. This article explains definition, properties, simple proofs, ex…

Vertical bar (|): symbol, mathematical and typographic uses Vertical bar Overview of the vertical bar glyph (|): names, mathematical meanings, computing uses, typographic variants, examples and distinctions.

Vinculum (mathematical symbol) Vinculum (symbol) A vinculum is a horizontal line used in mathematics to group expressions, mark repeating decimals, indicate fraction bars and radical scope, and to clarify the extent of an operati…

Vorticity: rotation and circulation in fluid flow Vorticity Vorticity measures local rotation in a fluid. This article explains its mathematical definition, physical meaning, historical background, common examples, and relevance in engineer…

Walter Benz (1931–2017) — German geometer and educator Walter Benz Walter Benz was a German mathematician known for work in geometry, academic posts in Germany and Canada, and the 2007 book 'Classical Geometries in Modern Contexts' on inner produc…

Walter Noll — German‑American mathematician and contributor to continuum mechanics Walter Noll Walter Noll (1925–2017) was a German‑born American mathematician noted for rigorous, axiomatic contributions to continuum mechanics and thermodynamics; professor emeritus at Carneg…

Wave equation: overview, mathematics, history and applications Wave equation A concise encyclopedia article on the wave equation: its form, properties, classical solutions, historical origins, common applications, and important variants in physics and engin…

Wavelet: functions for time–frequency analysis and multiscale signal representation Wavelet A wavelet is a localized oscillatory function used to analyze signals at multiple scales. This article covers core properties, historical origins, transforms, major families, and p…

Wavelet transform: concepts, types, and applications Wavelet transform A concise guide to the wavelet transform: continuous and discrete forms, dyadic scales, filter-bank interpretation, and common applications in compression, denoising and feature ex…

Weighted average (weighted mean) Weighted average A weighted average combines values with different levels of importance by multiplying each value by a weight and dividing by the total weight. Widely used in statistics, finance, g…

X-intercept (Cartesian graph) x-intercept Point(s) where a graph meets the x-axis; algebraically the real solutions of f(x)=0. Found by setting y=0 and solving. Important for graphing, root-finding and real-world interpret…

Xi (Ξ, ξ): the fourteenth Greek letter — form, history and uses Xi Xi (Ξ, ξ) is the 14th letter of the Greek alphabet, pronounced /ks/, valued 60 in Greek numerals, and an ancestor of Latin X and Cyrillic Ѯ; used in mathematics, physics and scient…

XSL attack (eXtended Sparse Linearization) — algebraic cryptanalysis of block ciphers XSL attack An algebraic attack that models a cipher as a large sparse system of quadratic equations and tries to recover keys by solving them; proposed for AES but never produced a practical…

Y (letter) Y Overview of the letter Y: its place in the Latin alphabet, history, roles as consonant and vowel, orthographic variants and common uses in English and other languages.

Y-intercept (coordinate geometry) y-intercept Point where a graph meets the y-axis. Definition, how to read or compute it from equations or points, special cases (vertical/horizontal lines), and practical interpretations in li…

Yahtzee: the classic five-dice game Yahtzee Yahtzee is a dice game for one or more players in which five dice are rolled up to three times per turn to make scoring combinations. It is widely played as a casual family and tou…

Year zero: calendrical conventions and their implications Year zero Explanation of the concept of year zero in different calendar systems, its historical origins, how astronomical and ISO standards use it, and practical effects on dating and interv…

Yodh (Yod, Yud) — the tenth letter of the Hebrew alphabet Yodh Yodh (י) is the tenth letter of the Hebrew alphabet, representing the consonant /j/ and the number 10. It is the smallest Hebrew letter and functions as a consonant, vowel marker a…

Yosemite Decimal System (YDS) Yosemite Decimal System A standardized scale used in North America to classify the technical difficulty and commitment of hikes and climbs, most commonly applied to rock climbing routes.

Yotta: the SI prefix for 10^24 Yotta- Yotta (symbol Y) is the largest official SI decimal prefix, denoting a factor of 10^24. Used for extremely large quantities in science and data, it was adopted as an SI prefix in 1…

Zermelo–Fraenkel set theory (ZF) Zermelo–Fraenkel set theory Zermelo–Fraenkel set theory (ZF) is the standard axiomatic framework for modern set theory; with the axiom of choice it is called ZFC. Covers axioms, origins, consequences and key…

Zero: the number, its properties, history and uses Zero Zero (0) denotes the absence of quantity. This article explains its mathematical role, properties, origin, uses in notation and computing, and common distinctions such as zero vers…

Zeta (Greek letter) Zeta Zeta (Ζ, ζ) is a letter of the Greek alphabet, representing the /z/ sound in modern Greek, with a numeric value of 7 and many uses in language, science, and symbol systems.

Zettabyte (ZB): unit of digital information Zettabyte A zettabyte is an SI data unit equal to 10^21 bytes. This article explains its size, relations to other units, historical context, examples and practical distinctions.

Zipf's law: rank–frequency power law in language and complex systems Zipf's law Zipf's law is an empirical rank–frequency rule—originally for words—stating frequency is approximately inversely proportional to rank; similar patterns appear across many natural a…