Mathematics

Phi (Φ φ): Greek letter — history, sounds, and uses Phi Phi, the 21st Greek letter (Φ φ), represents sounds, numbers and many scientific concepts. This article covers its origin, pronunciation changes, typographic forms and common mathe…

Pi (π): the circle constant and its role in mathematics Pi Pi (π) is the universal ratio of a circle's circumference to its diameter. An irrational, transcendental constant, it appears across geometry, analysis, probability and applied sci…

Pi (Greek letter Π, π) Pi (letter) Greek letter Pi (Π, π): its form and phonetic role, historical origin and descendants, numeric value in Greek numerals, and its distinct uses in mathematics as a product operator a…

Pie chart: definition, uses, and interpretation Pie chart A pie chart is a circular graphic that shows parts of a whole. This article explains how pie charts work, their history, common uses, strengths and limitations, and best practices…

Piecewise functions Piecewise A piecewise function is defined by different expressions on separate parts of its domain. This article explains notation, behavior at boundaries, common examples and uses in analys…

Pigeonhole principle A basic combinatorial rule: if more objects than boxes are distributed, some box contains multiple objects. Fundamental in proofs and applications across mathematics, computer scie…

Pint (unit of volume) Pint A pint is a traditional unit of volume used in Imperial and United States customary systems. It has distinct imperial, US liquid and US dry definitions and is commonly used for bev…

Pirc Defence A flexible hypermodern chess defence for Black against 1.e4, emphasizing a kingside fianchetto, delayed central confrontation and rich transpositional possibilities.

Place Value (Positional Notation) in Number Systems Place value Place value is the principle that a digit's position determines its value within a numeral. It underlies positional systems like decimal, binary and hexadecimal and enables efficie…

Plane (mathematics) A plane is a two-dimensional, perfectly flat surface extending without bound. It is a basic object in geometry and analytic geometry, used to model flat spaces and relations among…

Platonic Solids: The Five Regular Convex Polyhedra Platonic solid Platonic solids are the five convex regular polyhedra whose faces are identical regular polygons and whose vertices are all equivalent. They include the tetrahedron, cube, octahedr…

Plural (grammatical number) Plural Plural is the grammatical number category used to refer to more than one entity. This article explains forms, differences between count and mass nouns, irregular patterns, cross‑li…

Pocket Cube (2x2 Rubik's Cube variant) Pocket Cube A compact twisty puzzle consisting of eight corner pieces; a 2x2 version of the Rubik's Cube popular in speedsolving and as an introduction to cube algorithms.

Poincaré conjecture A central problem in geometric topology asking whether every closed, simply connected three-dimensional manifold is topologically a 3‑sphere; proved in the early 21st century with…

Point (concept and uses) Point A concise overview of the many meanings of 'point' across geometry, navigation, typography, finance, sports, natural features and more, with definitions, history, and common applic…

Point (geometry) A point is the basic notion of position in geometry: an entity without size that specifies location. This article explains its properties, notation, roles in different geometries,…

Poisson distribution A discrete probability distribution for counts of independent events in a fixed interval, determined by a single rate parameter λ; used to model rare or random event counts.

Polar coordinate system: definition, properties, and applications Polar coordinate system A two-dimensional coordinate system using a distance from a central point and an angle from a reference direction; covers definitions, conversions, common curves, uses, and key pro…

Polychoron (four-dimensional polytope) Polychoron A polychoron is a bounded four-dimensional polytope built from polyhedral cells. Overview, structure, classical regular examples, history, visualization methods, and mathematical s…

Polygon: definition, types, properties, history and uses Polygon An accessible overview of polygons: planar definitions, components, classifications (convex, concave, simple, complex), special spherical cases, historical context, and practical u…

Polyhedron A polyhedron is a three-dimensional solid with flat polygonal faces, straight edges, and vertices. Covers types (convex, concave, regular), basic formulas, history, examples, and a…

Polynomial (mathematics): definition, structure, uses and properties Polynomial A polynomial is an algebraic expression built from variables and coefficients using only addition, subtraction, multiplication and whole-number exponents. Overview, structure, hist…

Polynomial remainder theorem Statement, proof idea, examples and uses of the polynomial remainder theorem: the remainder when a polynomial is divided by x−a equals the polynomial's value at a.

Polynomial root (zero of a polynomial) Polynomial root A polynomial root (or zero) is a value of the variable that makes the polynomial evaluate to zero. Covers definition, multiplicity, complex roots, factorization, common methods to…

Polytope — geometric figure with flat sides in any number of dimensions Polytope A polytope is a geometric object bounded by flat faces in any dimension. Polygons, polyhedra and higher-dimensional polytopes (like the tesseract) appear across mathematics, optimi…

Population (statistics) In statistics, a population is the complete set of items or measurements under study. This article explains definitions, distinctions, sampling implications, examples, history, and…

Positive number An explanation of positive numbers: definition, notation, placement on the number line, common types, uses, and distinctions from related concepts.

Post hoc fallacy (post hoc ergo propter hoc) Post hoc fallacy The post hoc fallacy assumes that because one event follows another, the first caused the second. Explains the error, examples, related fallacies, consequences, and methods to dete…

Postfix notation (Reverse Polish Notation) Postfix notation Postfix notation (Reverse Polish Notation) writes operators after their operands, eliminating parentheses. It is evaluated with a stack and appears in calculators, programming lang…

Postulate: definition, role in reasoning, history and examples Postulate A postulate is a foundational statement accepted without proof that serves as a starting point for deductions. This article explains its nature, history, uses in mathematics and sc…

Power of Two (2^n): Definition, Properties, and Applications Power of two An explanation of powers of two—numbers of the form 2^n—covering definitions, key properties, examples, historical notes, and importance in binary systems, computing, and mathemati…

Power series: definition, convergence, and applications Power series A power series is an infinite polynomial in (x−c) with coefficients a_n. This article explains its definition, convergence (radius/interval), operations, historical context, and ma…

Power set (set of all subsets) Power set The power set of a set is the collection of all its subsets. It appears across mathematics: finite sets give 2^n members, and Cantor's theorem shows the power set is strictly large…

Numerical precision: decimal places, significant figures, and representation Precision (numbers) Numerical precision describes the fineness of a numeric value's digits or representation—measured by decimal places, significant figures, or digital formats. It differs from accura…

Predicate logic Predicate logic is the formal study of predicates, quantifiers, variables and relations; it extends propositional logic to express generality and structure in mathematics, linguist…

Prediction interval: definition, calculation, interpretation and uses Prediction interval A prediction interval gives a range where future individual observations are expected to fall with a specified probability, used in forecasting, regression and predictive inference…

Prefix (linguistics): meaning, types, and examples Prefix A prefix is an element added to the beginning of a word (or numeral) to alter its meaning. This article explains forms, common examples, historical notes, scientific use, and diffe…

Prefix notation (Polish notation) Prefix notation Prefix notation, or Polish notation, places operators before their operands. It is unambiguous without parentheses and is used in logic, programming (e.g., Lisp), calculators, and…

Primality test — methods for determining whether a number is prime Primality test Overview of primality tests: definitions, common algorithms (trial division, Fermat, Miller–Rabin, AKS), history, cryptographic uses, and certificates that verify primality.

Prime counting function (π(x)) Prime counting function The prime counting function π(x) returns the number of prime numbers less than or equal to x. This article explains its definition, basic properties, historical development, asympt…

Prime number A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. This article explains definitions, properties, history, tests, distribution…

Prime number theorem A concise account of the prime number theorem: its statement π(x) ~ x / ln x, historical development, main consequences for prime distribution, refinements and connections to the R…

Primitive root modulo n — generators of the multiplicative residue group Primitive root modulo n A primitive root modulo n is an integer that generates the multiplicative group of units modulo n. Article explains definition, existence, tests, examples and applications.

Principia Mathematica (Whitehead and Russell) Principia Mathematica A clear overview of Principia Mathematica, the early 20th-century three-volume attempt by Whitehead and Russell to reduce mathematics to logic, its structure, aims, influence, and…

Prism (geometry) A prism is a polyhedron formed by two congruent, parallel polygonal bases connected by parallelogram faces. This article explains types, properties, formulas and common examples an…

Probability: fundamental concepts, history, and practical applications Probability Overview of probability theory: basic definitions and rules, common examples (coins, dice), historical development, key theorems, interpretations, and major applications in science…

Probability density function A probability density function (pdf) describes how probability is distributed over continuous outcomes. It links to the cumulative distribution, expectations, common examples, and…

Probability distribution: definition, types, properties and applications Probability distribution An overview of probability distributions: what they are, discrete vs continuous types, main properties (PMF/PDF/CDF, expectation, variance), common examples, history and primary ap…