Mathematics

Figure‑eight: shape, movement, and knots Figure-eight Figure‑eight denotes the shape of the numeral 8 or the infinity sign and covers geometric curves, movement patterns in sports and dance, roller‑coasters, and several knots used in…

Finite (definition and uses) Finite An overview of the concept 'finite': meanings in everyday language and mathematics, basic formal definitions, historical and philosophical notes, and applications in computing, sci…

Finite set (mathematics) Finite set A finite set is a collection with a specific, limited number of elements. This article explains definitions, common characterizations, examples, historical context and why finite s…

First-order logic First order logic A concise, neutral overview of first-order logic: its syntax, semantics, core theorems, typical uses, and how it differs from propositional logic.

First-move advantage The competitive edge gained by the player who moves first in turn-based games—its causes, measurement in chess, historical debate, and methods games and designers use to compensate…

Fita — the Cyrillic letter Ѳ (historical glyph from Greek θ) Fita Fita (Ѳ, ѳ) is an historic Cyrillic letter derived from Greek theta, used for Greek loanwords and as the numeral nine in traditional Cyrillic numeration; now largely archaic except…

Five color theorem The five color theorem states that every planar map or planar graph can be colored using at most five colors so adjacent regions differ. It is a classical, well-understood result i…

Flattening (oblateness) of a spheroid Flattening Flattening (or oblateness) measures how much a rotating spheroid is squashed at the poles relative to its equator, important in geodesy, planetary science and mapping.

Flexagon: folded paper models that reveal hidden faces Flexagon A flexagon is a flat folded model, usually made from a paper strip, that can be 'flexed' to reveal hidden faces. Common types include hexaflexagons and tetraflexagons; used in puzz…

Floating-point representation in computers Floating point How computers represent real numbers using floating-point format: structure, history, uses, limitations, and practical guidance for numerical accuracy.

Fluid ounce A fluid ounce is a unit of volume used in the U.S. customary and imperial systems. The U.S. and imperial fluid ounces differ (≈29.57 mL vs ≈28.41 mL) and the term is distinct from…

Formal language A formal language is a precisely defined set of strings built from a fixed alphabet and governed by explicit formation rules, used in logic, computer science, mathematics and lingu…

Formula (mathematics and science) Formula A formula is a compact symbolic expression describing a relationship between quantities; used in mathematics, science and engineering for calculation, definition, and communication…

Fortnight — the 14‑day unit of time Fortnight A fortnight is a period of 14 days (two weeks). Widely used in British and Commonwealth English, it appears in scheduling, payroll and everyday speech; distinct from semimonthly an…

Four color theorem Statement and history of the four color theorem: its graph formulation, proof developments (including computer-assisted proofs), examples, related results, and why it matters in ma…

Fourier analysis: decomposition of functions into basic waves Fourier analysis Branch of mathematical analysis studying how functions or signals are represented as sums or integrals of oscillatory components. Includes Fourier series, transforms, discrete algo…

Fourier inversion theorem The Fourier inversion theorem states conditions under which a function can be reconstructed from its Fourier transform, with applications in analysis, PDEs, and signal processing.

Fourier Transform: Definition, Properties, History and Applications Fourier transform Comprehensive overview of the Fourier transform: its definition, intuition, principal properties, historical development, computation (DFT/FFT) and common applications in science a…

Fractal: Self-similarity, definitions, history and applications Fractal Overview of fractals: self-similar geometric sets, key properties (dimension, scaling), classic examples, history from Cantor to Mandelbrot, construction methods and practical uses…

Fraction A fraction expresses a part of a whole or a ratio between numbers, written as numerator over denominator; foundational in arithmetic, measurement, algebra, and probability.

Fraction (mathematics) A fraction expresses a part of a whole or a ratio between integers, using a numerator over a denominator. Covers notation, types, simplification, arithmetic rules, visual models, h…

Frequency distribution An overview of frequency distributions in statistics: what they are, how they are built for discrete and continuous data, common presentations, interpretation, and practical uses a…

Frequency (Frequentist) Interpretation of Probability Frequency probability Overview of the frequentist interpretation of probability: definition, foundations, history, common methods, applications and contrasts with other interpretations such as Bayesiani…

Function (mathematics, computing, biology, engineering, and social sciences) Function Overview of the concept of function across disciplines: definitions, types, examples, roles, and key distinctions in mathematics, computing, biology, engineering, and social scienc…

Function (mathematics) A function assigns to each element of one set exactly one element of another. Covers definition, notation, common properties, examples, historical notes, and practical uses.

Function composition: definition, properties, examples and applications Function composition Function composition combines two functions into one by feeding the output of the first into the second. This article explains notation, properties, examples, generalizations and c…

Function space A function space is a collection of functions from one set to another endowed with algebraic, topological or metric structure; central in analysis, PDEs, approximation and function…

Functional analysis Branch of mathematical analysis studying infinite-dimensional vector spaces, linear operators, and their applications in PDEs, quantum mechanics, numerical analysis and more.

Fundamental theorem of algebra Statement that every non-constant polynomial with complex coefficients has a complex root and therefore factors completely over the complex numbers.

Fundamental theorem of arithmetic Every integer greater than 1 factors uniquely as a product of prime numbers (up to order). This article explains the statement, examples, proof ideas, consequences and generalizati…

Fundamental Theorem of Calculus Principle linking differentiation and integration: the theorem that connects antiderivatives with definite integrals and explains how integration and differentiation undo each othe…

Furlong: traditional unit of distance Furlong A furlong is a historic English unit of distance equal to 660 feet (201.168 m). Once common in land measurement, it survives today in horse racing and some legal descriptions.

Fuzzy logic: degrees of truth, fuzzy sets, and practical uses Fuzzy logic Fuzzy logic extends classical true/false reasoning to degrees of truth. This article explains its basic ideas, mathematics, history, operations, applications and differences from p…

G (Latin letter) G G is the seventh letter of the Latin alphabet. This entry explains its shape, sounds in English, historical origin, typographic forms, computing codes, and common usages.

Gallon (unit of volume) Gallon A gallon is a non‑SI unit of liquid volume with several historical forms. Today the U.S. liquid gallon and the imperial gallon remain in common use; both differ in size and applica…

Galois field (finite field) Galois field A Galois field, or finite field, is a field with finitely many elements. They exist exactly for orders p^n and are fundamental in algebra, number theory, coding theory and cryptogr…

Gambler's fallacy: misconception about chance and independent events Gambler's fallacy The gambler's fallacy is the mistaken belief that past random events influence the probabilities of future independent outcomes; it affects gambling, investing and everyday risk ju…

Game theory: principles, history, and applications Game theory Game theory studies strategic decision-making among interdependent actors. It formalizes choices, payoffs and equilibria and is applied across economics, politics, biology, compute…

Gamma (Greek letter Γ, γ): history, notation, and common uses Gamma Gamma, the third Greek letter (Γ γ), represents the 'g' sound and the number 3; it appears across language, mathematics, physics, and engineering with several established notations…

Gamma function: extension of factorial and a central special function Gamma function Overview of the gamma function Γ(z): definition, basic properties, historical notes, common formulas, examples, and applications in mathematics and science.

Gauss–Bonnet theorem Gauss-Bonnet theorem A fundamental result linking curvature of a surface to its topology: the total curvature of a surface (plus boundary contribution) equals 2π times the Euler characteristic.

Geodesic (geometry and applications) Geodesic A geodesic is a curve representing the shortest or locally straightest path on a surface or manifold. This article explains definitions, equations, examples, history, and common us…

Geometric mean: definition, properties, history and applications Geometric mean The geometric mean is a multiplicative average of positive numbers, useful for growth rates, ratios and multiplicative processes. This article explains its definition, computation,…

Geometric topology: manifolds, knots, and embeddings Geometric topology Branch of topology concerned with manifolds, embeddings and the geometric structures and invariants that classify them, including knot theory, braid groups and low-dimensional resu…

Geometry: study of shapes, size, position and dimensions Geometry An informative overview of geometry: definitions, main branches, basic shapes, historical development, applications, and distinctions between flat and solid geometry.

Georg Cantor — founder of modern set theory Georg Cantor Georg Cantor (1845–1918) was a German mathematician who created set theory, introduced transfinite numbers and cardinalities, and posed the continuum hypothesis, profoundly shaping…

Gigasecond A gigasecond is one billion seconds (10^9 s), about 31.7 years. This article covers its definition, common conversions, notation, uses and distinctions from other large time units.

Girth (circumference measurement and practical uses) Girth Girth is the circumference of an object or body measured around its widest relevant cross-section. Used in forestry, shipping, clothing, and animal husbandry, with standard methods…