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Topics referred to by the same term
Area theorem may refer to: For Hawking's area theorem, see Black hole thermodynamics#Second law. For the area theorem in conformal mapping theory, see
Area_theorem
Relates areas of three parallelograms attached to three sides of an arbitrary triangle
Pappus's area theorem describes the relationship between the areas of three parallelograms attached to three sides of an arbitrary triangle. The theorem, which
Pappus's_area_theorem
Relation between sides of a right triangle
theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of
Pythagorean_theorem
The moment-area theorem is an engineering tool to derive the slope, rotation and deflection of beams and frames. This theorem was developed by Mohr and
Moment-area_theorem
Statement in complex analysis
analysis, a branch of mathematics, the Koebe 1/4 theorem states the following: Koebe Quarter Theorem. The image of an injective analytic function f :
Koebe_quarter_theorem
Formula for area of a grid polygon
In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points
Pick's_theorem
Gravitational-wave event
article. The discovery is empirical confirmation of Stephen Hawking's area theorem of 1971. It states that even though black holes lose energy from gravitational
GW250114
Perpendicular line segment from a triangle's side to opposite vertex
{\displaystyle h_{c}={\sqrt {pq}}} (geometric mean theorem; see special cases, inverse Pythagorean theorem) For acute triangles, the feet of the altitudes
Altitude_(triangle)
conformal mappings, the area theorem gives an inequality satisfied by the power series coefficients of certain conformal mappings. The theorem is called by that
Area theorem (conformal mapping)
Area_theorem_(conformal_mapping)
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
Matrix used in complex analysis
_{m=1}^{\infty }\sum _{n=1}^{N}\lambda _{n}c_{nm}z^{-m}\right).} Applying Milin's area theorem, ∑ m = 1 ∞ m | ∑ n = 1 N c m n λ n | 2 ≤ ∑ n = 1 N 1 n | λ n | 2 . {\displaystyle
Grunsky_matrix
Results on the surface areas and volumes of surfaces and solids of revolution
Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with
Pappus's_centroid_theorem
Mathematical theory
number of points removed. The Bers area inequality is a quantitative refinement of the Ahlfors finiteness theorem proved by Lipman Bers. It states that
Ahlfors_finiteness_theorem
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
Theorem about right triangles
In Euclidean geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hypotenuse in a right triangle
Geometric_mean_theorem
Equality of areas of a sliced disk
geometry, the pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way. The theorem is so called because
Pizza_theorem
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
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
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
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
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
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
Relates the length of a median of a triangle to the lengths of its sides
In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the
Apollonius's_theorem
Theorem in geometry
In Euclidean geometry, Varignon's theorem holds that the midpoints of the sides of an arbitrary quadrilateral form a parallelogram, called the Varignon
Varignon's_theorem
Equality of triangles between three squares
specifically geometry, Cross's theorem, also known as Vecten's theorem, equates the area of a triangle to the area of each of the triangles formed by
Cross's_theorem
Mathematical theorem
The theorem on friends and strangers is a mathematical theorem in an area of mathematics called Ramsey theory. Suppose a party has six people. Consider
Theorem on friends and strangers
Theorem_on_friends_and_strangers
Topics referred to by the same term
Pappus's theorem may refer to: Pappus's area theorem Pappus's centroid theorem Pappus's hexagon theorem This disambiguation page lists mathematics articles
Pappus's_theorem
Area ratio of one triangle and the triangle formed by the intersections of three cevians
Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of three cevians. The theorem states
Routh's_theorem
Mathematical theorem
In complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number
Riemann_mapping_theorem
Problem of constructing equal-area shapes
there must be a circle of equal area; this principle can be seen as a form of the modern intermediate value theorem. The more general goal of carrying
Squaring_the_circle
Mathematical proof by James Garfield
Garfield's proof of the Pythagorean theorem is an original proof of the Pythagorean theorem discovered by James A. Garfield, the 20th president of the
Garfield's proof of the Pythagorean theorem
Garfield's_proof_of_the_Pythagorean_theorem
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
Definite integral of a scalar or vector field along a path
identical to the vanishing of curl and divergence for F. By Green's theorem, the area of a region enclosed by a smooth, closed, positively oriented curve
Line_integral
Certain parallelograms occurring in a gnomon have areas of equal size
The theorem of the gnomon states that certain parallelograms occurring in a gnomon have areas of equal size. In a parallelogram A B C D {\displaystyle
Theorem_of_the_gnomon
High-area shapes can shift to hold many grid points
Blichfeldt's theorem is a mathematical theorem in the geometry of numbers, stating that whenever a bounded set in the Euclidean plane has area A {\displaystyle
Blichfeldt's_theorem
Theorem about triangles
otherwise. Ceva's theorem is a theorem of affine geometry, in the sense that it may be stated and proved without using the concepts of angles, areas, and lengths
Ceva's_theorem
Engineering method deriving slope and displacement of a beam
Essentially, it requires the same amount of computation as the moment-area theorems to determine a beam's slope or deflection; however, this method relies
Conjugate_beam_method
Theorem in planar dynamics
The parallel axis theorem, also known as Huygens–Steiner theorem, or just as Steiner's theorem, named after Christiaan Huygens and Jakob Steiner, can be
Parallel_axis_theorem
Theorem in calculus relating line and double integrals
In vector 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
Green's_theorem
Theorem in differential geometry
In differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying
Gauss–Bonnet_theorem
Ancient Greek mathematician (fl. 300 BC)
those concerning basic theorems and constructions of plane geometry and triangle congruence (1–26); parallel lines (27–34); the area of triangles and parallelograms
Euclid
Mathematical algorithm for calculating area of a simple polygon
Jacobi. The triangle form of the area formula can be considered to be a special case of Green's theorem. The area formula can also be applied to self-overlapping
Shoelace_formula
Theorem on polygon dissections
rotations. The Wallace–Bolyai–Gerwien theorem states that this can be done if and only if two polygons have the same area. Wallace had proven the same result
Wallace–Bolyai–Gerwien theorem
Wallace–Bolyai–Gerwien_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
Operation in calculus
this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides
Integral
Mathematical folklore
Macready substantively. In terms of how the NFL theorem is used in the context of the research area, the no free lunch in search and optimization is
No_free_lunch_theorem
Two theorems about families of holomorphic functions
In complex analysis, an area of mathematics, Montel's theorem refers to one of two theorems about families of holomorphic functions. These are named after
Montel's_theorem
Theorem on equilateral triangles
Viviani's theorem, named after Vincenzo Viviani, states that the sum of the shortest distances from any interior point to the sides of an equilateral
Viviani'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
Altitude (triangle) Area bisector of a triangle Angle bisector of a triangle Angle bisector theorem Apollonius point Apollonius' theorem Automedian triangle
List_of_triangle_topics
On inflection points of spherical curves
geometry, the tennis ball theorem states that any smooth curve on the surface of a sphere that divides the sphere into two equal-area subsets without touching
Tennis_ball_theorem
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
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
Theorem on an equilateral triangle constructed from three equilateral triangles
The difference in the areas of the outer and inner Napoleon triangles equals the area of the original triangle. The theorem is often attributed to Napoleon
Napoleon's_theorem
Theorem concerning uniform convergence
In measure theory, an area of mathematics, Egorov's theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of
Egorov's_theorem
On least area of curves of constant width
In plane geometry the Blaschke–Lebesgue theorem states that the Reuleaux triangle has the least area of all curves of given constant width. In the form
Blaschke–Lebesgue_theorem
Theorem in Euclidean geometry
In Euclidean geometry, Anne's theorem describes an equality of certain areas within a convex quadrilateral. This theorem is named after the French mathematician
Anne's_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
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
Gives conditions that guarantee the max–min inequality holds with equality
In the mathematical area of game theory and of convex optimization, a minimax theorem is a theorem that claims that max x ∈ X min y ∈ Y f ( x , y ) = min
Minimax_theorem
Explicitly describes the universal enveloping algebra of a Lie algebra
specifically in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal enveloping
Poincaré–Birkhoff–Witt theorem
Poincaré–Birkhoff–Witt_theorem
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
On topological spaces where the intersection of countably many dense open sets is dense
many areas of analysis and geometry, including some of the fundamental theorems of functional analysis. Versions of the Baire category theorem were first
Baire_category_theorem
Uniqueness theorem in complex analysis
In mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem which was discovered by Fritz David Carlson. Informally, it
Carlson's_theorem
Algebraic expansion of powers of a binomial
algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power ( x
Binomial_theorem
Approximation of a function by a polynomial
In calculus, Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree
Taylor's_theorem
Extremal graph theory bound on clique-free graph edges
In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given
Turán's_theorem
Three-dimensional analog of the Pythagorean theorem
In mathematics, De Gua's theorem is a three-dimensional analog of the Pythagorean theorem named after Jean Paul de Gua de Malves. It states that if a tetrahedron
De_Gua's_theorem
Gives the signature of a smooth compact oriented manifold in terms of Pontryagin numbers
differential topology, an area of mathematics, the Hirzebruch signature theorem (sometimes called the Hirzebruch index theorem) is Friedrich Hirzebruch's
Hirzebruch_signature_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
Statement on the gravitational attraction of spherical bodies
shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetric body. This theorem has particular
Shell_theorem
German structural engineer (1835–1918)
University Hannover Known for Mohr's circle Mohr–Coulomb theory Moment-area theorem Statically indeterminate structure Scientific career Fields Solid mechanics
Christian_Otto_Mohr
Topics referred to by the same term
particularly in the area of Fourier analysis, the Titchmarsh theorem may refer to: The Titchmarsh convolution theorem The theorem relating real and imaginary
Titchmarsh_theorem
Rational right triangles cannot have square area
Fermat's right triangle theorem is a non-existence proof in number theory, published in 1670 among the works of Pierre de Fermat, soon after his death
Fermat's right triangle theorem
Fermat's_right_triangle_theorem
Theorem that any three objects in space can be simultaneously bisected by a plane
mathematical measure theory, for every positive integer n the ham sandwich theorem states that given n measurable "objects" in n-dimensional Euclidean space
Ham_sandwich_theorem
Mathematical theorem
tiling. The theorem applies even if the complement of Γ {\displaystyle \Gamma } has additional components that are unbounded or whose area is not one;
Honeycomb_theorem
Equation for radii of tangent circles
In geometry, Descartes's theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic
Descartes's_theorem
On chains and antichains in partial orders
In mathematics, in the areas of order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size
Dilworth's_theorem
Topics referred to by the same term
algebra (a subject area in mathematics) Structure Theorem of Bass-Serre theory, a result in Geometric group theory. (another subject area in mathematics)
Structure_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
Visual mathematical proofs
Mamikon's theorem: The area of a tangent sweep is equal to the area of its tangent cluster, regardless of the shape of the original curve. The area of a cycloid
Visual_calculus
On the area enclosed by a point on a rigid chord rotating inside a convex closed curve
original curve, and that the area formula is the same as for that of the area of an ellipse with semi-axes p and q. The theorem's author was a president of
Holditch's_theorem
Characterizes the height of any finite partially ordered set
In mathematics, in the areas of order theory and combinatorics, Mirsky's theorem characterizes the height of any finite partially ordered set in terms
Mirsky'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)
On distances from opposite corners to a point inside a rectangle
In Euclidean geometry, the British flag theorem says that if a point P is chosen inside a rectangle ABCD then the sum of the squares of the Euclidean
British_flag_theorem
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It
Ancient_Greek_mathematics
All curves of constant width have the same perimeter
Barbier's theorem states that every curve of constant width has perimeter π times its width, regardless of its precise shape. This theorem was first published
Barbier's_theorem
Theorem that smooth bijections preserve dimension
In mathematical analysis, Netto's theorem states that continuous bijections of smooth manifolds preserve dimension. That is, there does not exist a continuous
Netto's_theorem
On when a space equals the closed convex hull of its extreme points
Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem—A compact convex
Krein–Milman_theorem
Theorem in topology
In topology, a discipline within mathematics, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every simple closed curve
Jordan_curve_theorem
One can't dissect a square into an odd number of triangles of equal area
In geometry, Monsky's theorem states that it is not possible to dissect a square into an odd number of triangles of equal area. In other words, a square
Monsky's_theorem
Branch of mathematics
accumulation of quantities and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. Calculus uses
Calculus
Every symmetric convex set in R^n with volume > 2^n contains a non-zero integer point
In mathematics, Minkowski's theorem is the statement that every convex set in R n {\displaystyle \mathbb {R} ^{n}} which is symmetric with respect to
Minkowski's_theorem
Swedish mathematician (1877–1932)
it appears in the Debye–Hückel theory Grönwall's area theorem Grönwall's inequality Grönwall's theorem Hille, Einar (1932). "Thomas Hakon Gronwall—In memoriam"
Thomas_Hakon_Grönwall
British mathematician who proved Fermat's Last Theorem
specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal
Andrew_Wiles
Book by Thomas Little Heath
bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Hinge theorem Inscribed angle theorem Intercept theorem Intersecting
A History of Greek Mathematics
A_History_of_Greek_Mathematics
Relates the 4 sides and 2 diagonals of a quadrilateral with vertices on a common circle
In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices
Ptolemy's_theorem
Theorem concerning ratios of line segments
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry
Intercept_theorem
Theorem in symplectic topology
Poincaré–Birkhoff theorem (also known as Poincaré–Birkhoff fixed point theorem and Poincaré's last geometric theorem) states that every area-preserving,
Poincaré–Birkhoff_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
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