Mathematics

Negative (concepts and applications) Negative Survey of the term “negative” across mathematics, logic, language, science, photography, medicine and systems, explaining meanings, notation, examples and important distinctions.

Negative number (definition, properties, arithmetic, and applications) Negative number Overview of negative numbers: definition, notation, position on the number line, arithmetic rules, history, practical uses, and common misconceptions.

Neusis construction: the marked‑ruler technique in classical geometry Neusis construction Neusis construction is an ancient Greek geometric method using a marked straightedge to place a segment of fixed length. It enabled solutions (e.g., angle trisection) beyond unmark…

Nim (mathematical impartial game) Nim Nim is an impartial combinatorial game in which players alternately remove counters from heaps. It is solved by binary xor (nim-sum); variants include bounded removals and misère p…

Nomogram: graphical calculators and alignment charts Nomogram Nomograms are two-dimensional graphical calculators that let users solve equations by aligning scales with a straightedge; historically important in engineering and still used for…

Geometries without Euclid's Parallel Postulate: Hyperbolic and Elliptic Systems Non-Euclidean geometry Overview of geometries that reject Euclid's parallel postulate, explaining hyperbolic and elliptic systems, their geodesics and curvature, key models, historical development, and a…

Nonagon (Enneagon) — the Nine‑Sided Polygon Nonagon A nonagon, also called an enneagon, is a polygon with nine sides and nine vertices. This article summarizes its geometry, regular-case formulas, symmetry, constructibility, star va…

Norm: meanings across social life, philosophy, mathematics, and culture Norm Comprehensive overview of the term “norm,” its uses in social science and philosophy, mathematical definitions, cultural and technical meanings, and notable examples.

Norm (mathematics): definition, examples, and applications Norm (mathematics) A norm assigns lengths to vectors in a vector space. This article explains the axioms, common norms (Euclidean, p‑norms, sup, absolute value), key properties, historical notes and…

Normal distribution (Gaussian distribution) Normal distribution A continuous probability distribution with a characteristic bell-shaped curve defined by mean and standard deviation; central to statistics and the central limit theorem.

Not: English negation, logical operator, and inverter Not An overview of 'not' as the basic negative particle in English, its grammatical role, logical and computing counterparts (negation, NOT gate), history, and common usages and distin…

Nothing: the concept of absence in philosophy, science, and mathematics Nothing An overview of 'nothing' as absence of things—exploring philosophical meanings, scientific vacuums, mathematical emptiness, historical development, distinctions, and common misconc…

NP-complete (computational complexity class) NP-complete NP-complete describes decision problems in NP that are at least as hard as every problem in NP; solving one in polynomial time would solve all NP problems in polynomial time.

NP-hardness (computational complexity) NP-hardness NP-hardness classifies decision and optimization problems that are at least as hard as the hardest problems in NP. It explains formal reductions, relation to NP-complete, examples,…

Null hypothesis in statistical hypothesis testing Null hypothesis A null hypothesis (H0) is a baseline statement used in statistical testing that presumes no effect or no difference; it is tested against data and rejected only when evidence is st…

Number (mathematical concept) Number An overview of numbers: their meanings, major classes (natural, integer, rational, real, complex, cardinal, ordinal), notation, history and principal uses in science and engineerin…

Number line: definition, structure, uses, and extensions Number line A number line is a geometric representation of real numbers on a straight line that shows order, distance, and scale; it underlies arithmetic, geometry, calculus and extends to the…

Number theory: concepts, history, and applications Number theory Number theory studies integers and their properties, including primes, divisibility, and equations. This article summarizes major topics, historical development, key theorems, and…

Numeral systems: ways of writing and organizing numbers Numeral system An overview of numeral systems: what they are, how they work, historical development, common examples (decimal, binary, Roman), and their uses in mathematics, computing and daily l…

Numerator (mathematics) Numerator The numerator is the top (or left) part of a fraction; this article explains its meaning, behavior in arithmetic and algebra, reduction and cancellation, examples, and related dist…

Numerical analysis: methods, history, and applications Numerical analysis Study of algorithms that compute approximate solutions to mathematical problems, covering methods, error control, historical origins, and applications in science, engineering, and…

Numerical digit A numerical digit is a written symbol used to represent a single place value in a positional numeral; this article explains digits, positional value, common sets (0–9), other bases…

Numerical integration (quadrature): methods, errors, and applications Numerical integration Overview of numerical integration (quadrature): common algorithms, historical notes, error behavior, multidimensional extensions and practical guidance for approximating definite i…

Numerical linear algebra: algorithms, stability, and applications Numerical linear algebra Branch of numerical analysis that develops and analyzes algorithms for matrix and vector computations: solving linear systems, eigenproblems, factorizations, stability, sparse meth…

Numerical Methods for Partial Differential Equations Overview of computational techniques used to approximate solutions of partial differential equations, covering main families of methods, analysis concepts, historical development,…

O (letter) O O is the fifteenth letter of the English alphabet, a vowel represented by a circular glyph; it has diverse pronunciations, a long written history from Semitic pictograms to Latin,…

Obelus (÷): symbol, history, forms and uses Obelus An obelus (÷) is the division sign; this article explains its shape, origins, historical uses, typographic variants, and where it appears today in maths, education and computing.

Obtuse angle An obtuse angle measures greater than 90° and less than 180° (π/2 to π radians). It contrasts with acute, right and straight angles and appears frequently in polygon geometry and t…

OCaml (Objective Caml) OCaml OCaml is a multi-paradigm programming language in the ML family that combines functional programming, strong static typing with type inference, imperative features, and an optional…

Octadecagon (18-sided polygon) Octadecagon An 18-sided polygon; the regular octadecagon has 160° interior angles, 20° central angles, symmetry D18, and area/side relations given by standard polygon formulas.

Octagon: definition, properties, history and practical uses Octagon An octagon is an eight-sided polygon. This article explains regular and irregular octagons, key measurements, symmetry, history, common applications and distinctions from related s…

Octahedron A polyhedron with eight faces. The regular octahedron has eight equilateral triangular faces, is dual to the cube, and appears in crystals, molecular structures, games, and design.

Octal numeral system (base 8) Octal Octal is the base‑8 numeral system using digits 0–7. It maps neatly to binary (3 bits per digit) and saw historical use in computing, some languages and file‑permission notation; h…

Odd number An odd number is an integer not divisible by two. This article explains definitions, properties, arithmetic rules, examples, uses, and historical and practical notes about odd numb…

Odds Odds express the chance of an event happening compared with the chance of it not happening. They are used in probability, gambling, statistics, and everyday language.

Omega (Greek letter Ω, ω) Omega Omega, the 24th letter of the Greek alphabet, represents the vowel sound 'o' and appears widely as a symbol in numerals, science, mathematics, engineering and culture.

Omicron: Greek letter Ο ο — form, history, and uses Omicron Omicron (Ο, ο) is a Greek letter representing the short 'o' sound. It has numeric value 70, gave rise to Latin and Cyrillic O, and appears in language, astronomy, and asymptotic no…

On-Line Encyclopedia of Integer Sequences (OEIS) On-Line Encyclopedia of Integer Sequences A comprehensive, community-maintained reference of integer sequences with searchable entries, formulas, references, program code, graphs and sonifications; originated by Neil J. A.…

One-way function A one-way function is easy to compute but hard to invert; central to modern cryptography, with variants like trapdoor functions and hash-like constructions used for signatures, has…

One's complement (bitwise inversion in binary arithmetic) Ones' complement One's complement is a binary bitwise inversion that flips every bit. Historically used to represent negative numbers and in some checksum algorithms; it has quirks such as two repr…

OpenOffice Math — Formula editor for the OpenOffice office suite OpenOffice Math OpenOffice Math is the formula editor bundled with the OpenOffice office suite. It creates and edits mathematical expressions for embedding in documents, supports many symbols and…

Operand (mathematics): definition, types, and usage Operand An operand is a value—such as a number or variable—that an operator acts on. This article explains operands, their roles in expressions, types (unary/binary/variadic), history, and…

Operation (mathematics) An operation is a rule or function that combines or transforms inputs (operands) into an output. This article explains types, arity, common examples, algebraic properties, uses and…

Opposite The concept of being opposite: denoting contrast, position across from, or mathematical/logical inverse. Explored in language (antonyms), mathematics (inverses), geometry, physics,…

Opposite number (additive inverse) Opposite number The opposite (additive inverse) of a number is the value which, when added to the original, yields zero. This article explains its definition, properties, examples, and extensions…

Order of magnitude A concise explanation of orders of magnitude: what they mean, how to compute and use them, historical context, common examples, and how they differ from precise comparisons.

Order of operations (operator precedence and associativity) Order of operations Rules that determine the sequence in which parts of an expression are evaluated, including precedence, associativity, parentheses, common mnemonics, and differences in programming…

Order theory: partial orders, lattices, and applications Order theory Mathematical study of order relations on sets: definitions (partial, total, strict), common structures (posets, lattices, well-orders), history, examples, and applications in mathe…