6,052 articles
Pierre de Fermat
Pierre de Fermat (1601–1665) was a French lawyer in Toulouse who did mathematics as an amateur, founding modern number theory and probability, and stating Fermat's Last Theorem.
Pierre-Simon Laplace
Pierre-Simon Laplace, marquis de Laplace, was a French mathematician and astronomer who proved the stability of the solar system, founded modern probability theory, and proposed the nebular hypothesis.
Pigeonhole principle
The pigeonhole principle, also called the Dirichlet box principle, states that more than n objects placed in n boxes force one box to hold two or more.
Pigpen cipher
The pigpen cipher, also called the masonic cipher, is a geometric substitution cipher that replaces letters with grid symbols, used by Freemasons since the 18th century.
Pitman–Yor process
The Pitman–Yor process, also known as the two-parameter Poisson–Dirichlet process, is a Bayesian nonparametric prior over probability measures that generalizes the Dirichlet process by adding a discount parameter, producing power-law behavior useful in language modeling.
Pivot element
A pivot element, central to complete pivoting and other pivoting strategies, is the entry by which Gaussian elimination divides rows below it to create zero multipliers.
Placebo control
A placebo control is an inactive comparison group in a clinical trial, used with randomization and blinding to distinguish a drug's effect from the placebo effect.
Plackett–Burman design
A Plackett–Burman design is a two-level screening design of experiments, introduced by Plackett and Burman in 1946, that estimates the main effects of many factors in few runs.
Plactic monoid
The plactic monoid, or tableau algebra, is the monoid of semistandard Young tableaux with multiplication by insertion; two words are equal exactly when Schensted's algorithm gives the same tableau.
Planar algebra
A planar algebra is an algebraic structure of vector spaces acted on by planar diagrams, introduced by Vaughan Jones in 1999 to axiomatize subfactor invariants.
Planar graph
A planar graph is a graph that can be drawn in the plane with no edge crossings. Planarity is a property of the graph itself, not of one drawing.
Planarization
Planarization is the process of turning a non-planar graph into a planar one by removing edges or replacing crossings with vertices, used in graph drawing and circuit design.
Plane
In geometry, a plane is a two-dimensional flat surface, one of the basic undefined objects, with the point and line, on which geometry is built.
Plane partition
A plane partition is a partition of an integer n whose parts are arranged in a two-dimensional array, weakly decreasing across rows and down columns.
Platonic solid
A Platonic solid, also called a regular solid, is a convex polyhedron with identical regular polygon faces meeting at each vertex; exactly five exist: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
Playfair cipher
The Playfair cipher, or Playfair square, is a manual letter-pair encryption scheme invented by Charles Wheatstone in 1854 and used by British forces in several wars.
Plethysm
Plethysm is an operation on symmetric functions, written f[g], in which one symmetric function is substituted into another, introduced by D. E. Littlewood in 1936.
Plücker coordinates
Plücker coordinates are the homogeneous coordinates of a subspace in projective geometry: the maximal minors of a matrix spanning it, first considered by Julius Plücker in 1869.
Plünnecke–Ruzsa inequality
The Plünnecke–Ruzsa inequality is a theorem in additive combinatorics stating that if |A+B| ≤ K|A|, then |kB − ℓB| ≤ K^(k+ℓ)|A|, proved by Plünnecke in 1970 and Ruzsa in 1989.
Plus and minus signs
The plus sign (+) and minus sign (−) are mathematical symbols for addition and subtraction, first printed in 1489 in Johannes Widmann's Leipzig arithmetic book.
Plus–minus sign
The plus or minus symbol (±) is a mathematical sign indicating a value may be either added or subtracted, also used to report measurement uncertainty.
PNAD
PNAD (Pesquisa Nacional por Amostra de Domicílios) is a Brazilian household sample survey run by the IBGE since 1967; its successor, the PNAD Contínua (2012), is Brazil's headline unemployment source.
Pochhammer symbol
The Pochhammer symbol, also called the shifted factorial, is the notation (a)n for the rising factorial a(a+1)(a+2)⋯(a+n-1); in combinatorics it can instead mean the falling factorial.
Poincaré algebra
The Poincaré algebra is the ten-dimensional Lie algebra of the Poincaré group, the symmetry group of flat spacetime, named for Henri Poincaré, who studied the group in 1905.
Poincaré conjecture
The Poincaré conjecture, also called Smale's second problem, states that every closed, simply connected 3-dimensional manifold is the 3-sphere; Grigori Perelman proved it in 2002.
Poincaré disk model
The Poincaré disk model is a conformal model of hyperbolic geometry in which the hyperbolic plane is drawn as the interior of a circle, introduced by Eugenio Beltrami in 1868.
Poincaré duality
Poincaré duality is a theorem of algebraic topology stating that on a closed orientable n-manifold, the k-th cohomology group is isomorphic to the (n − k)-th homology group.
Poincaré half-plane model
The Poincaré half-plane model represents hyperbolic geometry on the upper half of the complex plane, where geodesics are vertical lines and semicircles meeting the real axis at right angles.
Poincaré homology sphere
The Poincaré homology sphere, also called the Poincaré dodecahedral space, is a closed 3-manifold with the same homology as the 3-sphere, whose nontrivial fundamental group disproved Poincaré's 1900 claim.
Poincaré inequality
The Poincaré inequality, a result in Sobolev space theory named after Henri Poincaré, bounds a function's size on a bounded domain by the size of its gradient.