Examples

An instance of a concept.

Ideas 301–431 of 431.

Name	Kind	Subject
Hopf fibration	Example	Algebraic topology
Penrose tiling	Example	Convex and discrete geometry
Exceptional Lie group E8	Example	Topological groups, Lie groups
Rössler attractor	Example	Ordinary differential equations
Hypernetted-chain equation	Example	Statistical mechanics, structure of matter
Gauss map	Example	Number theory
Lippmann–Schwinger equation	Example	Quantum theory
Real projective plane	Example	Geometry
Wallpaper group	Example	Group theory and generalizations
Ackermann function	Example	Mathematical logic and foundations
The cosets of a subgroup that is not normal do not form a group	Example	Group theory and generalizations
Smale horseshoe	Example	Dynamical systems and ergodic theory
Wilkinson's polynomial	Example	Numerical analysis
Surface of revolution	Example	Differential geometry
Swallowtail catastrophe	Example	Global analysis, analysis on manifolds
Poincaré homology sphere	Example	Manifolds and cell complexes
Variety of lattices	Example	Order, lattices, ordered algebraic structures
Tetration	Example	Real functions
Sierpiński space	Example	General topology
Hypercube	Example	Convex and discrete geometry
Sierpiński carpet	Example	General topology
Particular values of the gamma function	Example	Special functions
Airy equation	Example	Ordinary differential equations
Hopf surface	Example	Several complex variables and analytic spaces
Rudin–Shapiro polynomials	Example	Harmonic analysis on Euclidean spaces
Doubling on the integers is not an isomorphism	Example	Group theory and generalizations
Sawtooth wave	Example	Harmonic analysis on Euclidean spaces
Noncommutative torus	Example	Functional analysis
SL(2,R)	Example	Topological groups, Lie groups
Meyer wavelet	Example	Harmonic analysis on Euclidean spaces
Kempner series	Example	Sequences, series, summability
Hankel transform of radial functions in the plane	Example	Integral transforms, operational calculus
Logistic map	Example	Dynamical systems and ergodic theory
Space-filling curve	Example	General topology
Counting measure	Example	Measure and integration
Tamari lattice	Example	Order, lattices, ordered algebraic structures
The symmetric group S3 is not abelian	Example	Group theory and generalizations
Lorentz group	Example	Topological groups, Lie groups
Ising model	Example	Statistical mechanics, structure of matter
Representation theory of the Lorentz group	Example	Topological groups, Lie groups
Coiflet	Example	Harmonic analysis on Euclidean spaces
The natural numbers under addition are not a group	Example	Group theory and generalizations
Iterated exponentiation	Example	Sequences, series, summability
Laplace transform of a power function	Example	Integral transforms, operational calculus
Grassmannian as classifying space	Example	Algebraic topology
Steiner chain	Example	Geometry
Poincaré half-plane model	Example	Geometry
Dihedral quandle	Example	Manifolds and cell complexes
Segre embedding	Example	Algebraic geometry
Fuller's phenomenon	Example	Calculus of variations and optimal control; optimization
Semiautomaton as a unary algebra	Example	General algebraic systems
Dirichlet distribution	Example	Probability theory and stochastic processes
Median algebra as a ternary algebra	Example	General algebraic systems
Quintic equation	Example	Field theory and polynomials
Octonionic projective plane	Example	Geometry
Affine plane over a finite field	Example	Geometry
Tsirelson space	Example	Functional analysis
Arithmetic progression	Example	Number theory
Mellin transform of a theta series and the zeta function	Example	Number theory
Duffing equation	Example	Ordinary differential equations
Carleman's singular integral equation	Example	Integral equations
Fundamental domain of the modular group	Example	Number theory
Permutohedron	Example	Convex and discrete geometry
Fatou–Bieberbach domain	Example	Several complex variables and analytic spaces
The alternating group A3 is normal in S3	Example	Group theory and generalizations
Green's function of the ball	Example	Potential theory
Möbius–Kantor configuration	Example	Combinatorics
Square wave	Example	Harmonic analysis on Euclidean spaces
Crown	Example	Order, lattices, ordered algebraic structures
The alternating group is the kernel of the sign	Example	Group theory and generalizations
Taft algebra	Example	Associative rings and algebras
Whitehead link	Example	Manifolds and cell complexes
Asymmetric simple exclusion process	Example	Probability theory and stochastic processes
Basel problem via Fourier series	Example	Harmonic analysis on Euclidean spaces
Kepler problem	Example	Mechanics of particles and systems
1 − 1 + 2 − 6 + 24 − 120 + ⋯	Example	Sequences, series, summability
Pin group	Example	Topological groups, Lie groups
Geodesic flow	Example	Dynamical systems and ergodic theory
The odd integers are not a subgroup of the integers	Example	Group theory and generalizations
Pseudo-arc	Example	General topology
Weaire–Phelan structure	Example	Convex and discrete geometry
Cusp catastrophe	Example	Global analysis, analysis on manifolds
Cantor algebra	Example	Order, lattices, ordered algebraic structures
Wilson–Cowan neural field equation	Example	Biology and other natural sciences
Trefoil knot	Example	Manifolds and cell complexes
Pappus configuration	Example	Combinatorics
Reeb foliation	Example	Manifolds and cell complexes
d'Alembert's equation	Example	Ordinary differential equations
Legendre's equation	Example	Ordinary differential equations
Airfoil equation	Example	Integral equations
Stiefel manifold	Example	Algebraic topology
Besicovitch set of measure zero	Example	Measure and integration
Laplacian on the Sierpiński gasket	Example	Potential theory
Laplace transform method for the heat equation	Example	Integral transforms, operational calculus
Space of null sequences	Example	Functional analysis
Van der Pol oscillator	Example	Ordinary differential equations
Category of sets	Example	Category theory; homological algebra
Laplace transform of the Heaviside step function	Example	Integral transforms, operational calculus
Menger sponge	Example	General topology
Diffeomorphism group	Example	Global analysis, analysis on manifolds
Morlet wavelet	Example	Harmonic analysis on Euclidean spaces
Borromean rings	Example	Manifolds and cell complexes
Lorenz system	Example	Ordinary differential equations
Laplace transform of the exponential function	Example	Integral transforms, operational calculus
Padua points	Example	Approximations and expansions
A subgroup of order two in S3 is not normal	Example	Group theory and generalizations
Face lattice	Example	Convex and discrete geometry
Sturmian word	Example	Computer science
Torus as a group	Example	Topological groups, Lie groups
List of small groups	Example	Group theory and generalizations
Orders of the elements of S3	Example	Group theory and generalizations
Voter model	Example	Probability theory and stochastic processes
Hill differential equation	Example	Ordinary differential equations
Chandrasekhar's X- and Y-functions	Example	Integral equations
1 + 1 + 1 + 1 + ⋯	Example	Sequences, series, summability
Exceptional Lie group G2	Example	Topological groups, Lie groups
Bunimovich stadium	Example	Dynamical systems and ergodic theory
Lieb–Liniger integral equation	Example	Statistical mechanics, structure of matter
Doob martingale	Example	Probability theory and stochastic processes
Hopf manifold	Example	Several complex variables and analytic spaces
Fourier series of Bernoulli polynomials	Example	Harmonic analysis on Euclidean spaces
Hermite equation	Example	Ordinary differential equations
Flexible polyhedron	Example	Convex and discrete geometry
Laplace transform of a periodic function	Example	Integral transforms, operational calculus
Runge's phenomenon	Example	Approximations and expansions
Hilbert transform of sinusoids	Example	Integral transforms, operational calculus
Hofstadter sequences	Example	Number theory
Conway knot	Example	Manifolds and cell complexes
Category of small categories	Example	Category theory; homological algebra
Free magma	Example	General algebraic systems
Heisenberg group	Example	Topological groups, Lie groups