Mathematics

Cauchy sequence A Cauchy sequence is a sequence in which elements become arbitrarily close to each other as the sequence progresses. It formalizes internal convergence and is central to completene…

Cellular automaton: definition, structure, history, and applications Cellular automaton A cellular automaton is a discrete model of computation and dynamical systems built from a grid of simple cells that update by local rules; used in mathematics, computer science, p…

Cent (currency subunit, musical interval, land measure and other meanings) Cent Overview of 'cent' as a one‑hundredth unit in money, music, South Asian land measure, typography and related historical and regional uses.

Central limit theorem A fundamental result in probability and statistics describing how sums or averages of many independent random variables tend toward a normal distribution under broad conditions.

Century: definition, history, naming and related terms Century A century is a span of 100 years. This article explains the term’s meaning, Latin roots, Roman military origin, calendar numbering conventions, anniversaries (centenary/centennial)…

Century leap year (Gregorian rule) Century leap year In the Gregorian calendar, a century leap year is a year divisible by 400. This article explains the rule, examples, historical context, weekday patterns and how it differs from th…

Chain (unit of length) Chain (unit) A chain is a historical unit used mainly in surveying and land measurement. The best known form, Gunter's chain, equals 66 feet (20.1168 m) and connects directly to acres, furlongs…

Chain rule (differential calculus) Chain rule The chain rule gives the derivative of a composition of functions. It links the rate of change of an outer function to the inner function's rate and is essential in single- and mul…

Chaos theory: sensitive dependence and unpredictable behavior in dynamical systems Chaos theory Study of deterministic systems that show extreme sensitivity to initial conditions, producing complex, often fractal patterns; important in weather, physics, biology, engineering a…

Chess and Computers: history, technology, and impact Chess and computers Overview of the relationship between chess and computing: origins, technical approaches, milestones, uses in training and research, and how engines differ from human play.

Chess endgame The chess endgame is the final phase of a game when few pieces remain. This article explains its defining features, common types, historical development, practical techniques, and…

Chess rating system An overview of systems used to estimate chess players' playing strength, their history, how ratings are calculated and adjusted, common variants, and practical uses and limitations…

Chi (Greek letter χ): shape, sound, numeric value and uses Chi (letter) Chi (Χ, χ) is the 22nd letter of the Greek alphabet. It denotes a voiceless velar or palatal fricative in Greek, has the numeral value 600, and appears widely in mathematics, stati…

Chi-square distribution (χ²): definition, properties, and applications Chi-square distribution A continuous probability distribution for the sum of squared standard normals. Explains definition, degrees of freedom, main properties, history and common statistical uses such as…

Chiliagon (1000-sided polygon) Chiliagon A chiliagon is a polygon with 1000 sides and 1000 vertices. This article explains its properties, formulas for area and side length, symmetry, constructibility, and philosophical a…

Chinese postman problem (route inspection problem) Chinese postman problem Combinatorial optimization problem: find the shortest closed walk that traverses every edge of a graph at least once. Solvable in polynomial time for undirected graphs; important i…

Chinese remainder theorem A theorem in number theory describing existence and construction of integers solving systems of congruences; used in computation, cryptography, and algebraic structure of modular a…

Chomsky hierarchy A classification of formal grammars and languages into four nested types (0–3), relating each class to restrictions on production rules and equivalent automata used in computation…

Chosen-plaintext attack (CPA): methods, significance, and defenses Chosen-plaintext attack A chosen-plaintext attack (CPA) is a cryptanalysis model where an adversary can request ciphertexts for plaintexts of their choosing. This article explains types, examples, securit…

Church–Turing thesis A foundational claim in computability theory: any effectively calculable function can be computed by a Turing machine. Explains formal meanings, history, consequences, and notable…

Circle — definition, parts, formulas, properties and uses Circle A circle is the set of points in a plane at a fixed distance from a center. This article explains terminology, key formulas (circumference and area), basic properties, history, and…

Circumference: length around a closed curve, especially a circle Circumference Circumference is the distance around a closed curve — for circles the familiar C = 2πr or C = πd — and is central to geometry, measurement, engineering, and arc-length calculations…

Clockwise (direction of rotation) Clockwise Movement around a circle that follows the same direction as the hands of an analog clock; used as a standard orientation in clocks, mechanics, navigation and everyday description.

Closure (computer programming) A closure is a function together with a saved surrounding environment that preserves bound variables across calls. It enables data hiding, callbacks, and higher-order programming.

Coding theory: structure, history, and applications in communication and storage Coding theory Coding theory studies the design and analysis of codes for reliable, efficient information representation — including error detection/correction, compression, and roles in cryptogr…

Coefficient (mathematics) Coefficient A coefficient is a multiplicative factor that scales a variable, function, vector or operator. This article explains types, roles in polynomials, series and equations, and common d…

Collatz conjecture: definition, history, examples and significance Collatz conjecture An overview of the Collatz conjecture: the simple iterative rule 3n+1 for odd n and n/2 for even n, its origin, partial results, examples, why it is hard, and its role in mathemati…

Combination: meanings, types, and applications across fields Combination Overview of the term “combination,” its main senses in mathematics, games, locks, equestrian sports, martial arts, and cultural uses, with key distinctions and examples.

Combination (mathematics) A combination counts the ways to choose k items from n without regard to order. Explains notation, the binomial coefficient, formulas, examples, variations, properties, and common…

Combinatorial game theory Mathematical study of finite, deterministic, perfect-information games. Covers impartial and partizan games, Sprague–Grundy theory, surreal numbers, disjunctive sums, and applicati…

Combinatorial optimization: theory, problems, and methods Combinatorial optimization Study of selecting the best discrete configuration from a finite or countable set. Covers common problems (TSP, MST, matching), algorithmic methods, complexity, and applications.

Combinatorics: concepts, methods, and applications Combinatorics An introduction to combinatorics covering its main themes, typical problems and methods, historical notes, and key applications in mathematics, computer science, and related fields…

Common year (calendar) Common year A common year is a calendar year that is not a leap year. In the Gregorian system it has 365 days and shifts weekdays by one; contrast with leap years and other calendar systems.

Common year starting on Saturday — calendar characteristics and examples Common year starting on Saturday Details of a common (365-day) year whose January 1 falls on Saturday: weekday layout, month starts, holiday dates, Friday the 13th pattern, ISO-week effects, Gregorian/Julian notes…

Common year starting on Sunday (calendar pattern) Common year starting on Sunday Overview and practical details for a common (365-day) year whose January 1 falls on Sunday — habitually characterized by Doomsday on Tuesday and specific holiday placements.

Common year beginning on Thursday — calendar layout, examples and notable effects Common year starting on Thursday Explanation of a common (365-day) year whose January 1 falls on Thursday: layout, occurrences of Friday the 13th, holiday dates, examples in Gregorian and Julian calendars, and ISO…

Common year beginning on Wednesday (calendar pattern) Common year starting on Wednesday Encyclopedic overview of a common (365-day) year whose January 1 falls on Wednesday: monthly starts, Friday the 13th behavior, holidays, examples in Gregorian and Julian calendars,…

Commutative property Mathematical property stating that order of operands does not affect result for certain operations, most commonly addition and multiplication; contrasts with noncommutative operati…

Commutative ring A commutative ring is an algebraic structure with addition and a commutative multiplication that distributes over addition; it is a foundational object in algebra, number theory, a…

Comparison of the Imperial and U.S. customary measurement systems Comparison of the Imperial and US customary systems Concise comparison of the Imperial and U.S. customary systems: origins, principal units, principal differences in volume and mass, common conversions, and contemporary usage.

Drafting Compass (pair of compasses) Compass (drafting) A drafting compass is a two‑legged instrument for drawing circles and arcs, measuring and transferring distances; used in geometry, technical drawing, surveying, navigation and map…

Complementary angles Angles whose measures sum to a right angle (90° or π/2 radians); important in geometry and trigonometry and distinct from supplementary angles.

Complex analysis Branch of mathematical analysis studying functions of complex numbers, focusing on holomorphic (analytic) functions, contour integrals, singularities, conformal maps and applicatio…

Complex number A complex number pairs a real part and an imaginary part, written a + bi, forming a two-dimensional number system central to algebra, geometry, analysis, physics and engineering.

Complex plane A clear, compact overview of the complex plane: its structure, coordinate systems, history, common operations, and applications in science and engineering.

Complex system A complex system is an arrangement of interacting components whose collective behavior exhibits properties not evident from the parts alone, studied across science, engineering, an…

Complexity class A complexity class groups computational problems that require comparable algorithmic resources (time, space, randomness). It organizes problems by difficulty and underpins theoreti…

Computational complexity theory Complexity theory The study of the resources (time, space, randomness) required to solve computational problems, how algorithms are classified, and the relationships between problem classes includin…