6,052 articles
Rete algorithm
The Rete algorithm, also called the Rete network, is an efficient pattern-matching algorithm for production rule systems, developed by Charles Forgy at Carnegie Mellon University from 1974.
Retrospective cohort study
A retrospective cohort study, also called a historical cohort study, is an observational study that uses existing records to identify past exposures and trace outcomes forward to the present.
Reuleaux triangle
The Reuleaux triangle, named for Franz Reuleaux, is a curve of constant width built from an equilateral triangle, and it has the smallest area of any constant-width curve.
Reverse mathematics
Reverse mathematics, also known as reverse math, is a program in mathematical logic founded by Harvey Friedman in 1974 that determines which axioms are necessary to prove theorems of ordinary mathematics.
Reverse Polish notation
Reverse Polish notation, also called postfix notation, writes operators after their operands, so no parentheses or precedence rules are needed; 1 + 2 becomes 1 2 +.
Reversible-jump Markov chain Monte Carlo
Reversible-jump Markov chain Monte Carlo (RJMCMC) is a Bayesian computation method, introduced by Peter J. Green in 1995, that lets the number of parameters change during sampling.
Rhind Mathematical Papyrus
The Rhind Mathematical Papyrus, also known as the Ahmes Papyrus, is an ancient Egyptian mathematics textbook with 84 problems, copied by the scribe Ahmose around 1650 BC.
Rhombic dodecahedron
The rhombic dodecahedron is a convex polyhedron with 12 rhombic faces, 24 edges, and 14 vertices, first described by Johannes Kepler around 1600. It tiles three-dimensional space with no gaps.
Rhombic triacontahedron
The rhombic triacontahedron is a convex polyhedron with 30 golden rhombic faces and 32 vertices, the dual of the icosidodecahedron and one of the 13 Catalan solids, discovered by Kepler.
Rhombicosidodecahedron
The rhombicosidodecahedron, formally the small rhombicosidodecahedron, is an Archimedean solid with 62 faces: 20 triangles, 30 squares, and 12 regular pentagons, named by Johannes Kepler in 1619.
Rhombicuboctahedron
The rhombicuboctahedron, also called the small rhombicuboctahedron, is an Archimedean solid with 26 faces, 8 triangles and 18 squares, first drawn by Leonardo da Vinci in 1509.
Rhombus
A rhombus (plural rhombi), often called a diamond or lozenge, is a quadrilateral with four equal sides, and its diagonals bisect each other at right angles.
Ri Jong-yol
Ri Jong-yol (리정렬), who renamed himself Lee Jung-ho, is a North Korean defector and math prodigy who won four straight International Mathematical Olympiad silver medals before defecting in 2016.
Riccati equation
The Riccati equation is a first-order ordinary differential equation, quadratic in the unknown function, named for the Venetian mathematician Jacopo Riccati and published in 1724.
Ricci curvature
Ricci curvature, also called the Ricci tensor, is a geometric quantity on a Riemannian manifold measuring how volumes change, introduced by Gregorio Ricci-Curbastro in 1904.
Ricci flow
Ricci flow is a geometric evolution equation introduced by Richard Hamilton in 1982 that smooths a manifold's metric, and underlies Perelman's proof of the Poincaré conjecture.
Ricci soliton
A Ricci soliton is a self-similar solution of the Ricci flow whose metric changes only by scaling and diffeomorphisms, generalizing Einstein metrics and modeling singularities.
Rice–Shapiro theorem
The Rice–Shapiro theorem characterizes the semi-decidable index sets of partial computable functions: a property is semi-decidable exactly when it is upward closed and witnessed by finite subfunctions.
Rice's theorem
Rice's theorem, also called the Rice–Myhill–Shapiro theorem, states in computability theory that every nontrivial semantic property of programs is undecidable, proved by Henry Gordon Rice in 1953.
Richard B. Lehoucq
Richard B. Lehoucq is an American computational mathematician at Sandia National Laboratories in Albuquerque, known for the ARPACK and Anasazi eigenvalue libraries and a 2024 SIAM Fellowship.
Richard M. Friedberg
Richard M. Friedberg is an American theoretical physicist and logician at Columbia University known for solving Post's problem in 1957 and for an early 1958 paper on machine learning.
Richardson extrapolation
Richardson extrapolation is a numerical analysis technique that combines approximations at different step sizes to cancel the leading error term, named after Lewis Fry Richardson.
Ridge regression
Ridge regression, also known as Tikhonov regularization, is a penalized linear regression method introduced by Hoerl and Kennard in 1970 that trades bias for lower variance.
Riemann curvature tensor
The Riemann curvature tensor, also called the Riemann-Christoffel tensor, is a four-index tensor measuring the intrinsic curvature of a manifold through path-dependent parallel transport; it is central to general relativity.
Riemann hypothesis
The Riemann hypothesis, also called the Riemann conjecture, is an unproved 1859 conjecture stating that all nontrivial zeros of the Riemann zeta function have real part 1/2.
Riemann integral
The Riemann integral, also called Riemann integration, defines the integral of a bounded function over a finite interval through lower and upper sums; Bernhard Riemann introduced it in 1854.
Riemann mapping theorem
The Riemann mapping theorem states that any simply connected proper plane domain can be conformally mapped onto the open unit disk, formulated by Bernhard Riemann in 1851.
Riemann problem
The Riemann problem is an initial value problem for a hyperbolic partial differential equation with piecewise constant data, whose jump breaks up into waves; it underlies Godunov-type numerical methods.
Riemann solver
A Riemann solver is a numerical method that computes fluxes in finite-volume schemes for hyperbolic conservation laws by solving the Riemann problem at each cell interface.
Riemann sphere
The Riemann sphere, also called the extended complex plane, is the complex plane with one point at infinity added, modeled as a sphere by stereographic projection.