Mathematics

Square root The square root of a number is a value that, when squared, yields the original number. This article explains definitions, notation, real and complex roots, computation methods, and…

Square root of 2 The positive number whose square equals 2; an irrational constant with geometric, algebraic, and historical significance, commonly written √2 and approximately 1.41421356.

Square yard (yd²): definition, conversions, history and usage Square yard The square yard (yd²) is an imperial/US customary unit of area equal to a square one yard on a side. This article explains its definition, common conversions, history, uses, and di…

Standard deviation (measure of dispersion) Standard deviation Standard deviation quantifies how spread out values are around the mean. It is the square root of variance, used in statistics, science, finance and quality control, with different…

Standard error: meaning, calculation, and applications Standard error The standard error measures the variability of a statistic's sampling distribution. This article explains its definition, common formulas, interpretation, history, and typical uses…

Statistical parameter A statistical parameter is a fixed numerical characteristic of a probability distribution or population; this article explains its role, common types, notation, relation to estimat…

Statistical significance An explanation of statistical significance: definition, history, how p-values and significance levels are used, common misunderstandings, and practical recommendations for research…

Statistical survey An organized method for collecting information from a population or sample to estimate characteristics, test hypotheses, and support decision-making across science, government, and…

Statistician A statistician designs studies, extracts meaning from data, and applies probability and inference across science, industry, and government to inform decisions, measure uncertainty,…

Statistics: the mathematical study of collecting and interpreting data Statistics Statistics is the discipline that describes, summarizes and draws conclusions from data. It encompasses methods for measurement, inference, modeling and communication across many d…

Steradian: the SI unit of solid angle Steradian The steradian (symbol sr) is the SI derived unit for solid angle. It measures the portion of space around a point subtended by an area on a sphere and is widely used in photometry,…

Stereographic projection A classical geometric projection mapping a sphere minus one point onto a plane; angle-preserving, circle-preserving, and fundamental in complex analysis, cartography, and several a…

Stigma (Greek letter and numeral) Stigma (letter) Stigma (Ϛ, ϛ) is a historic Greek ligature of sigma+tau that became a distinct symbol used also as the numeral for six; it appears in manuscripts, typography, and the Greek numeral…

Stochastic process: concepts, types, and applications Stochastic process An introduction to stochastic processes: random time-ordered systems used to model evolving phenomena in finance, science and engineering, with core ideas, history, and common exam…

Straight: geometric concept, optics, language, and common usages Straight Explains 'straight' as a geometric property, its role in optics, linguistic senses (direct, consecutive, heterosexual), historical roots, and everyday examples and distinctions.

Straightedge and compass construction Classical geometric constructions made with an unmarked straightedge and a compass: methods, limits, algebraic characterization, classical examples, and key impossibility results.

Stream cipher A stream cipher is a symmetric-key algorithm that encrypts data one unit at a time by combining plaintext with a pseudorandom keystream; widely used for low-latency and resource-co…

String: material object, technical concept, and cultural term String Comprehensive overview of 'string' as a physical cord and its meanings in science, computing, music, and everyday life, with history, construction, uses, and distinctions.

Structured Query Language (SQL): Overview, Components, History, and Uses Structured Query Language Structured Query Language (SQL) is the standard language for defining, querying, and modifying data in relational databases. This article explains its parts, history, features, and…

Student's t-distribution: definition, properties, history, and applications Student's t-distribution A continuous probability distribution used for inference with small samples; describes behavior of sample means, underpins t-tests, confidence intervals, and appears in regression…

Student's t-test A statistical procedure for comparing means: one-sample, paired, and two-sample variants; includes assumptions, interpretation, history, uses, and common limitations.

Subset (mathematics) Subset Explanation of subsets: definitions, notation, examples, properties and distinctions such as proper subset and relation to power sets, aimed at a general mathematical audience.

Subset sum problem Decision problem: given integers and a target, decide whether some subset sums to the target. Important in complexity theory, algorithms, cryptography and combinatorial optimizatio…

Substitution box (S-box) in symmetric cryptography Substitution box An S-box (substitution box) is a nonlinear component used in symmetric block ciphers to provide confusion by mapping input bits to output bits; designs balance nonlinearity, invert…

Substitution–Permutation Network (SPN): Structure, Design, and Uses Substitution-permutation network A substitution–permutation network (SPN) is a layered construction used in block cipher design combining nonlinear substitution and linear permutation to achieve confusion and diff…

Subtraction: the arithmetic operation of taking differences Subtraction Subtraction is the arithmetic process of finding the difference between quantities. This article explains notation, core properties, common algorithms, extensions to vectors and ma…

Sudoku: the logic-based number-placement puzzle Sudoku Sudoku is a logic puzzle in which the solver fills a grid so each row, column and region contains the required digits without repetition. Widely published in print and digital form…

Sum (mathematics) Sum An explanation of the mathematical concept of a sum: definition, notation, properties, types (finite and infinite), examples, and key applications across arithmetic, algebra and an…

Sun Tzu (Sun Zi) — Chinese mathematician and author of the Sunzi Suan Jing Sun Tzu (mathematician) Sun Tzu (Sun Zi) was a Chinese mathematician of the third century CE, known for the Sunzi Suan Jing and an early statement of the Chinese remainder theorem; he studied calendar and…

Surface (geometry and physical layer) Surface A surface is the outermost layer or a two-dimensional shape. This article explains physical and mathematical meanings, main properties, historical context, and practical uses in sc…

Surface area: definition, calculation, and applications Surface area Surface area measures the total area of an object's outer surface. This article explains what it means, how it is calculated for common solids, why it matters, and important distin…

Surface integral An explanation of surface integrals: definitions, parametrization and computation, scalar vs vector integrals (flux), historical context, common applications in physics and enginee…

Surface-area-to-volume ratio The relationship between an object's surface area and its volume; explains how size and shape affect heat transfer, diffusion, reaction rates, biology, and engineering through scal…

Surjective function (onto): definition, examples, properties, and distinctions Surjective function A surjective (onto) function maps every element of its codomain to at least one element of its domain. This article explains the definition, examples, equivalent characterizations,…

Symmetric-key algorithm Overview of symmetric-key algorithms: principles, types (stream and block), modes, key management, common ciphers, cryptanalysis, applications, performance and implementation consi…

Symmetry: concepts, types, history and applications Symmetry Overview of symmetry in mathematics, science, art and nature — types (reflection, rotation, translation), symmetry elements, historical development, uses, and key distinctions like…

System of Linear Equations Overview of systems of linear equations: definitions, structure, solution types and common methods, brief history, and practical applications across science and engineering.

System of measurement An organized framework of units, standards and methods used to assign numeric quantities to physical, economic, or other properties for science, engineering and commerce.

System of units An organized set of measurement units and rules that relate quantities. Covers base and derived units, coherent systems, common examples (SI, CGS, imperial), history, uses, and sta…

T (letter) T T is the twentieth letter of the English alphabet, representing a voiceless alveolar stop and appearing widely in writing, phonetics, typography, and symbolic notation.

Talent (unit of mass and money) Talent (measurement) An ancient unit of mass and money used across the Mediterranean and Near East, the talent varied by culture and era; it served as a standard for large quantities of metal and for f…

Tangent (mathematics and geometry) Tangent Concepts of 'tangent' in mathematics and everyday language: touching at a point, the trig function tan, tangent lines and planes, tangent spaces, key properties, and common uses.

Tangent (geometry) A tangent is a straight line that touches a curve at a point and shares its instantaneous direction. It formalizes the idea of 'touching' in geometry and calculus and is used for a…

Tau (Greek letter τ) Tau Tau (Τ, τ) is the 19th letter of the Greek alphabet, representing the 't' sound. It has the numeric value 300 and has given rise to letters such as Latin T and Cyrillic Т.

Tautology in Propositional Logic — Definition, Examples, and Contrasts Tautology (logic) Explore tautology in propositional logic: clear definition, truth-table verification, canonical examples like excluded middle, contrasts with contradiction and contingency, and eve…

Taxicab number A taxicab number is the smallest integer expressible as the sum of two positive cubes in n distinct ways; the name comes from a famous Hardy–Ramanujan anecdote about 1729.

Taylor series: local power-series expansions and practical approximations Taylor series A Taylor series represents a function near a point as an infinite power series built from its derivatives. Used to approximate and analyse functions in calculus, physics, engineeri…

Taylor's theorem: polynomial approximation and remainder forms Taylor's theorem Taylor's theorem describes how a sufficiently differentiable function can be approximated near a point by a polynomial; it also gives formulas controlling the approximation error a…