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Relation between sides of a right triangle
2 + b 2 = c 2 . {\displaystyle a^{2}+b^{2}=c^{2}.} The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been
Pythagorean_theorem
Correlation of a signal with a time-shifted copy of itself, as a function of shift
\ldots ,T-1,} the theorem gives ∑ h = 1 T − 1 ρ ^ ( h ) = − 1 2 , {\displaystyle \sum _{h=1}^{T-1}{\hat {\rho }}(h)=-{\frac {1}{2}},} provided that the
Autocorrelation
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
Theorem in calculus relating line and double integrals
calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R 2 {\displaystyle
Green's_theorem
Fundamental theorem in probability theory and statistics
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample
Central_limit_theorem
One of several theorems in different areas of mathematics
mathematics, Schur's theorem is any of several theorems of the mathematician Issai Schur. In differential geometry, Schur's theorem is a theorem of Axel Schur
Schur's_theorem
Theorem in differential topology
The hairy ball theorem of algebraic topology (formally, the Sphere Vector Field Theory, sometimes called the hedgehog theorem) states that there is no
Hairy_ball_theorem
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem, or the sampling theorem, is a theorem in the field of signal processing which serves as a fundamental bridge between
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Continuous function on an interval takes on every value between its values at the ends
In mathematical analysis, the intermediate value theorem states that if f {\displaystyle f} is a continuous function whose domain contains the interval
Intermediate_value_theorem
In mathematics, a statement that has been proven
mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses
Theorem
Rational-number approximation of a real number
Perron 1913, Chapter 2, Theorem 15 Hurwitz 1891, p. 284 Hardy & Wright 1979, Chapter 10.11 See Perron 1929, Chapter 2, Theorem 23, p. 63 Hardy & Wright
Diophantine_approximation
Relationship between derivatives and integrals
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Integers have unique prime factorizations
mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
A prime p divides a^p–a for any integer a
In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In
Fermat's_little_theorem
Theorem in graph theory
In the mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can
2-factor_theorem
About simultaneous modular congruences
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then
Chinese_remainder_theorem
Proposition in probability theory
Probability and measure. New York: John Wiley & Sons. ISBN 0-471-00710-2. (Theorem 34.4) Christopher Sims, "Notes on Random Variables, Expectations, Probability
Law_of_total_expectation
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. Brouwer. It states that for any continuous function f {\displaystyle
Brouwer_fixed-point_theorem
Group of mathematical theorems
specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients
Isomorphism_theorems
Method for finding limits in calculus
calculus, the squeeze theorem (also known as the sandwich theorem, the two policemen and a drunk theorem among other names) is a theorem regarding the limit
Squeeze_theorem
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Theorem on modular exponentiation
In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers
Euler's_theorem
1995 publication in mathematics
Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Theorems that help decompose a finite group based on prime factors of its order
specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow
Sylow_theorems
Result about when a matrix can be diagonalized
In linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented
Spectral_theorem
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
Operations in formal language theory
2, p.60 Hopcroft, Ullman (1979), Sect.3.2, Theorem 3.4, p.60 Hopcroft, Ullman (1979), Sect.6.2, Theorem 6.2, p.131 Hopcroft, Ullman (1979), Sect.3.2,
String_operations
Well-quasi-ordering of finite trees
In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under
Kruskal's_tree_theorem
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating
Mean_value_theorem
Mathematical result or axiom on order relations
axiom of choice). The principle is also called the Hausdorff maximality theorem or the Kuratowski lemma. The Hausdorff maximal principle states that, in
Hausdorff_maximal_principle
Conditions under which a chaotic system can be reconstructed by observation
In the study of dynamical systems, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence
Takens's_theorem
Mathematical rule for inverting probabilities
In probability theory, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (/beɪz/), gives a mathematical rule for inverting
Bayes'_theorem
Statement about integration on manifolds
generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about
Generalized_Stokes_theorem
Theorem in economics
Coase theorem (/ˈkoʊs/) postulates the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem is significant
Coase_theorem
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x
Implicit_function_theorem
Geometry theorem relating line segments created by a secant and tangent line
equation holds: | P T | 2 = | P G 1 | ⋅ | P G 2 | {\displaystyle |PT|^{2}=|PG_{1}|\cdot |PG_{2}|} The tangent-secant theorem can be proven using similar
Tangent–secant_theorem
Theorem about the range of an analytic function
In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after
Picard_theorem
Theorem in vector calculus
Stokes' theorem, also known as the Kelvin–Stokes theorem, is a theorem in vector calculus that relates the behavior of a vector field along the edge of
Stokes'_theorem
Theorem in mathematics
In mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that
Inverse_function_theorem
17. Theorem (Joyal lifting). Haugseng, Theorem 5.3.1. Kapulkin & Voevodsky 2020, Theorem 2.10 Land 2021, Theorem. 2.1.8 Joyal 2002, Theorem 2.2 Joyal
Joyal's extension and lifting theorems
Joyal's_extension_and_lifting_theorems
On triangles inscribed in a circle with a diameter as an edge
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle
Thales's_theorem
Number of intersection points of algebraic curves and hypersurfaces
Bézout's theorem is a statement concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that
Bézout's_theorem
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
On distances from opposite corners to a point inside a rectangle
opposite corners. As an equation: A P 2 + C P 2 = B P 2 + D P 2 . {\displaystyle AP^{2}+CP^{2}=BP^{2}+DP^{2}.} The theorem also applies to points outside the
British_flag_theorem
Bounded sequence in finite-dimensional Euclidean space has a convergent subsequence
In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result
Bolzano–Weierstrass_theorem
Tool for analyzing divide-and-conquer algorithms
In the analysis of algorithms, the master theorem for divide-and-conquer recurrences provides an asymptotic analysis for many recurrence relations that
Master theorem (analysis of algorithms)
Master_theorem_(analysis_of_algorithms)
Existence and uniqueness of solutions to initial value problems
known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard,
Picard–Lindelöf_theorem
Algebraic expansion of powers of a binomial
the binomial theorem are: ( x + y ) 0 = 1 , ( x + y ) 1 = x + y , ( x + y ) 2 = x 2 + 2 x y + y 2 , ( x + y ) 3 = x 3 + 3 x 2 y + 3 x y 2 + y 3 , ( x +
Binomial_theorem
In economics, the Debreu's theorems are preference representation theorems—statements about the representation of a preference ordering by a real-valued
Debreu's representation theorems
Debreu's_representation_theorems
On the transcendence of a large class of numbers
from the theorem: Gelfond–Schneider constant 2 2 = 2.665144142 … {\displaystyle 2^{\sqrt {2}}=2.665144142\ldots } and its square root 2 2 = 2 2 = 1.632526919
Gelfond–Schneider_theorem
Theorem on the orders of subgroups
In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is
Lagrange's theorem (group theory)
Lagrange's_theorem_(group_theory)
Conditions for switching order of integration in calculus
Fubini's theorem gives the conditions under which a double integral can be computed as an iterated integral, i.e. by integrating in one variable at a
Fubini's_theorem
Sufficiently long sequences of numbers have long monotonic subsequences
In mathematics, the Erdős–Szekeres theorem asserts that, given r {\displaystyle r} and s {\displaystyle s} , any sequence of distinct real numbers with
Erdős–Szekeres_theorem
Theorem about metric spaces
Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important
Banach_fixed-point_theorem
Statement in mathematical combinatorics
In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours)
Ramsey's_theorem
Characterization of how many integers are prime
( x ) {\displaystyle \log _{e}(x)} . In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of prime numbers among the
Prime_number_theorem
On distances between points on a circle
three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places n {\displaystyle n} points on a circle, at angles of θ , 2 θ ,
Three-gap_theorem
Existence of group elements of prime order
In mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G (the number
Cauchy's theorem (group theory)
Cauchy's_theorem_(group_theory)
Theorem in real analysis
derivative is zero. The theorem is named after Michel Rolle. The theorem is a special case of, and is used to prove, the mean value theorem. If a real function
Rolle's_theorem
Meromorphic function on the complex plane
Theory. Chapter 7, Section 2, Theorem 2.1, 1992, p. 455. Neukirch: Algebraic Number Theory. Chapter 7, Section 2, Theorem 2.1, 1992, p. 455. Neukirch:
L-function
Planar maps require at most four colors
In mathematics, the four color theorem, or the four-color map theorem, states that no more than four colors are required to color the regions of any map
Four_color_theorem
2013 film by Terry Gilliam
The Zero Theorem is a 2013 science fiction film directed by Terry Gilliam, starring Christoph Waltz, David Thewlis, Mélanie Thierry and Lucas Hedges.
The_Zero_Theorem
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no group decision-making
Arrow's_impossibility_theorem
Concept in topology
2., § 4. Wall 2016, § A.4. Editorial note: why is "paracompact" needed? Hirsch 1997, Ch. 2., § 4., Theorem 4.2. Hirsch 1997, Ch. 2., § 2., Theorem 2.6
Mapping_space
No spontaneous symmetry breaking in two-dimensional systems at finite temperature
Hohenberg–Mermin–Wagner theorem or Mermin–Wagner theorem (also known as Mermin–Wagner–Berezinskii theorem or Mermin–Wagner–Coleman theorem) states that continuous
Mermin–Wagner_theorem
Counts 0s of a vector field on a differentiable manifold using its Euler characteristic
Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem in differential
Poincaré–Hopf_theorem
Condition under which an odd prime is a sum of two squares
1 2 + 2 2 , 13 = 2 2 + 3 2 , 17 = 1 2 + 4 2 , 29 = 2 2 + 5 2 , 37 = 1 2 + 6 2 , 41 = 4 2 + 5 2 . {\displaystyle 5=1^{2}+2^{2},\quad 13=2^{2}+3^{2},\quad
Fermat's theorem on sums of two squares
Fermat's_theorem_on_sums_of_two_squares
Non-fiction book by Simon Singh
Fermat's Last Theorem. Review of Fermat's Enigma by Andrew Bremner (1998), MR 1491363. Radford, Tim (2 August 2013), "Fermat's Last Theorem by Simon Singh
Fermat's_Last_Theorem_(book)
In algebra, expression of an ideal as the intersection of ideals of a specific type
In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection
Primary_decomposition
Mathematical folklore
In mathematical folklore, the "no free lunch" (NFL) theorem (sometimes pluralized) of David Wolpert and William Macready, alludes to the saying "no such
No_free_lunch_theorem
Formula for area of a grid polygon
points, so its area is A = 7 + 8 2 − 1 = 10 {\displaystyle A=7+{\tfrac {8}{2}}-1=10} square units. One proof of this theorem involves subdividing the polygon
Pick's_theorem
Characterization by prime factors of sums of two squares
In number theory, the sum of two squares theorem relates the prime decomposition of any integer n > 1 to whether it can be written as a sum of two squares
Sum_of_two_squares_theorem
Physics theorem
Mathematically, the theorem states that ⟨ T ⟩ = − 1 2 ∑ k = 1 N ⟨ F k ⋅ r k ⟩ , {\displaystyle \langle T\rangle =-{\frac {1}{2}}\,\sum _{k=1}^{N}\langle
Virial_theorem
About maxima and minima of functions
theorem states that any local extremum of a real function at which it is differentiable is a stationary point. It is also known as Fermat's theorem,
Interior_extremum_theorem
Number of solutions of linear systems in terms of matrix ranks
Rouché–Capelli theorem is a theorem in linear algebra that determines the number of solutions of a system of linear equations, given the ranks of its augmented
Rouché–Capelli_theorem
On topological spaces where the intersection of countably many dense open sets is dense
The Baire category theorem (BCT) is an important result in general topology and functional analysis. The theorem has two forms, each of which gives sufficient
Baire_category_theorem
Graphical aid for deriving some concepts in combinatorics
dots and dividers) is a graphical aid for deriving certain combinatorial theorems. It can be used to solve a variety of counting problems, such as how many
Stars and bars (combinatorics)
Stars_and_bars_(combinatorics)
Theorem in statistics and econometrics
In statistics and econometrics, the Frisch–Waugh–Lovell (FWL) theorem is a property of ordinary least squares estimators. Named for econometricians Ragnar
Frisch–Waugh–Lovell_theorem
Ties Euler characteristic of a closed even-dimensional Riemannian manifold to curvature
In mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that
Chern–Gauss–Bonnet_theorem
On line segments from a point to the vertices of an equilateral triangle
Pompeiu's theorem is a result of plane geometry, discovered by the Romanian mathematician Dimitrie Pompeiu. The theorem is simple, but not classical.
Pompeiu's_theorem
Polynomial zeros related to linear factors
In algebra, the factor theorem connects polynomial factors with polynomial roots. Specifically, if f ( x ) {\displaystyle f(x)} is a (univariate) polynomial
Factor_theorem
Theorem in electrical circuit analysis
stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources
Thévenin's_theorem
Infinitely many prime numbers exist
Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proven by Euclid
Euclid's_theorem
Upper bound on intersecting set families
element. The Erdős–Ko–Rado theorem states that when n {\displaystyle n} is large enough for the problem to be nontrivial ( n ≥ 2 r {\displaystyle n\geq 2r}
Erdős–Ko–Rado_theorem
Every set is smaller than its power set
{\displaystyle n} elements has a total of 2 n {\displaystyle 2^{n}} subsets, and the theorem holds because 2 n > n {\displaystyle 2^{n}>n} for all non-negative integers
Cantor's_theorem
Gives the average curvature of any closed convex plane curve
Fenchel's theorem is an inequality on the total absolute curvature of a closed smooth space curve, stating that it is always at least 2 π {\displaystyle 2\pi
Fenchel's_theorem
Theorem in mathematics
In mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square
Parseval's_theorem
Type of mathematical space
§5.6 Robinson 1996, Theorem 4.1.13 Arkhangel'skii & Fedorchuk 1990, Theorem 5.2.3 Arkhangel'skii & Fedorchuk 1990, Theorem 5.2.2 Arkhangel'skii & Fedorchuk
Compact_space
Generalization of Pythagorean theorem
\\[3mu]a^{2}&=b^{2}+c^{2}-2bc\cos \alpha ,\\[3mu]b^{2}&=a^{2}+c^{2}-2ac\cos \beta .\end{aligned}}} The law of cosines generalizes the Pythagorean theorem, which
Law_of_cosines
Theorem in harmonic analysis
and L 2 {\displaystyle L^{2}} , then the Plancherel theorem states that f ^ {\displaystyle {\hat {f}}} also belongs to L 2 {\displaystyle L^{2}} , and
Plancherel_theorem
Theorem in set theory
In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there
Schröder–Bernstein_theorem
Says when a natural number is the sum of three squares of integers
theorem states that a natural number can be represented as the sum of three squares of integers n = x 2 + y 2 + z 2 {\displaystyle n=x^{2}+y^{2}+z^{2}}
Legendre's three-square theorem
Legendre's_three-square_theorem
Concept in number theory
In number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for any real numbers α
Dirichlet's approximation theorem
Dirichlet's_approximation_theorem
Theorem in complex analysis
In complex analysis, Liouville's theorem states that every bounded entire function must be constant. That is, every holomorphic function f {\displaystyle
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
Condition for a linear operator to be open
functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem (named after Stefan Banach and Juliusz
Open mapping theorem (functional analysis)
Open_mapping_theorem_(functional_analysis)
Extension of Lidskii's theorem
so-called 2 3 {\displaystyle {\tfrac {2}{3}}} -nuclear operators. The theorem was proven in 1955 by Alexander Grothendieck. Lidskii's theorem does not
Grothendieck_trace_theorem
Three-dimensional analog of the Pythagorean theorem
Gua's theorem can be applied for proving a special case of Heron's formula. The Pythagorean theorem and de Gua's theorem are special cases (n = 2, 3) of
De_Gua's_theorem
Relates the length of a median of a triangle to the lengths of its sides
| 2 + | A C | 2 = 2 ( | B D | 2 + | A D | 2 ) . {\displaystyle |AB|^{2}+|AC|^{2}=2(|BD|^{2}+|AD|^{2}).} It is a special case of Stewart's theorem. For
Apollonius's_theorem
Proof assistant and programming language
Inductive Constructions), the foundational type theory developed with the Coq theorem prover, which was renamed to Rocq in 2024. It is a free and open-source
Lean_(proof_assistant)
travel, tourism, insurance
2 THEOREM
2 THEOREM
Surname or Lastname
North German variant of Laas 2.Jewish (Ashkenazic)
North German variant of Laas 2.Jewish (Ashkenazic) : unexplained.English : nickname from Middle English lesse, lasse ‘smaller’ (from Old English lǣssa ‘less’), perhaps also used in the sense ‘younger’.
Surname or Lastname
English
English : variant of Hayden 2.
Surname or Lastname
English
English : variant of Hackett 2.
Surname or Lastname
English
English : variant of Maul 2.
Surname or Lastname
English
English : patronymic from Lamb 2.
Surname or Lastname
Variant of Nicolai 2.English
Variant of Nicolai 2.English : variant of Nicholas.
Surname or Lastname
English
English : patronymic from Lamb 2.
Surname or Lastname
English
English : variant of Diamond 2.
Surname or Lastname
English
English : variant of Mixon 2.
Surname or Lastname
English
English : patronymic from Lamb 2.
Surname or Lastname
English
English : variant of Garrett 2.
Surname or Lastname
English
English : variant of Glad 2.
Surname or Lastname
English
English : variant of Greenfield 2.
Surname or Lastname
English
English : patronymic from Lakin 2.
Boy/Male
Shakespearean
King Henry IV, Part 1' Earl of March. Scroop.
Surname or Lastname
English
English : variant of Haddock 2.
Girl/Female
Indian
Mixture of 2 Names
Surname or Lastname
English
English : variant of Land 2.
Surname or Lastname
English
English : variant of Goodall 2.
Surname or Lastname
English
English : patronymic from Lamb 2.
2 THEOREM
2 THEOREM
2 THEOREM
2 THEOREM
2 THEOREM
2 THEOREM
2 THEOREM
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