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Geometric relation between a triangle's side lengths and cevian length
In geometry, Stewart's theorem yields a relation between the lengths of the sides and the length of a cevian in a triangle. Its name is in honour of the
Stewart's_theorem
Topics referred to by the same term
the 17th century Stewart's Lane was a nineteenth century road in London that gave its name to Stewarts Lane railway stations Stewarts Lane locomotive depot
Stewart's
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
Subfield of set theory
This fact—that all closed games are determined—is called the Gale–Stewart theorem. Note that by symmetry, all open games are determined as well. (A game
Determinacy
Line intersecting both a vertex and opposite edge of a triangle
Ceva, who proved a theorem about cevians which also bears his name. The length of a cevian can be determined by Stewart's theorem: in the diagram, the
Cevian
Geometrical theorem relating the lengths of two segments that divide a triangle
In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that
Angle_bisector_theorem
Northern Irish physicist (1928–1990)
John Stewart Bell (28 July 1928 – 1 October 1990) was a physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum
John_Stewart_Bell
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
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
Theorem about triangles
In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle △ABC, let the lines AO, BO, CO be drawn from the vertices to a common
Ceva's_theorem
Problem-solving technique in geometry
{3}{13}}={\tfrac {7}{26}}.} Cevian Ceva's theorem Menelaus's theorem Stewart's theorem Angle bisector theorem Routh's theorem Barycentric coordinates Lever Rhoad
Mass_point_geometry
Topics referred to by the same term
known as Jaguar Racing, now known as Red Bull Racing Stewart's theorem, a geometry theorem Stewart–Tolman effect, physics Sewart Air Force Base Steuart
Stewart
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
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 (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
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 in physics
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with
Bell's_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
Scottish mathematician (1717–1785)
what is now known as Stewart's theorem, which relates measurements on a triangle to an additional line through a vertex. Stewart also provided a solution
Matthew Stewart (mathematician)
Matthew_Stewart_(mathematician)
Equations of degree 5 or higher cannot be solved by radicals
In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial
Abel–Ruffini_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
Invariance under simultaneous charge conjugation, parity transformation and time reversal
this theorem is sometimes known as the Lüders–Pauli theorem. At about the same time, and independently, this theorem was also proved by John Stewart Bell
CPT_symmetry
Theorem in descriptive set theory
In descriptive set theory, the Borel determinacy theorem states that any Gale–Stewart game whose payoff set is a Borel set is determined, meaning that
Borel_determinacy_theorem
Theorem that every set can be well-ordered
In mathematics, the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict
Well-ordering_theorem
Economic theory about capital structure
The Modigliani–Miller theorem (of Franco Modigliani, Merton Miller) is an influential element of economic theory; it forms the basis for modern thinking
Modigliani–Miller_theorem
Macroeconomic trade theorem
The Heckscher–Ohlin theorem is one of the four critical theorems of the Heckscher–Ohlin model, developed by Swedish economist Eli Heckscher and Bertil
Heckscher–Ohlin_theorem
Method for finding limits in calculus
calculus, the squeeze theorem (also known as the sandwich theorem, the two policeman and a drunk theorem among other names) is a theorem regarding the limit
Squeeze_theorem
2 "Out of Asia" 25 September 1997 (1997-09-25) 3 "Fermat's Last Theorem" 2 October 1997 (1997-10-02) 4 "The Virus That Cures" 9 October 1997 (1997-10-09)
List of Horizon (British TV series) episodes
List_of_Horizon_(British_TV_series)_episodes
Evaluates a line integral through a gradient field using the original scalar field
The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated
Gradient_theorem
Matthew Stewart publishes Some General Theorems of Considerable use in the Higher Parts of Mathematics, including an account of Stewart's theorem on the
1746_in_Scotland
Certain vector fields are the sum of an irrotational and a solenoidal vector field
In physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector
Helmholtz_decomposition
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
Basic result in harmonic analysis on compact topological groups
In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are
Peter–Weyl_theorem
Mathematical connection between field theory and group theory
between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group
Galois_theory
Two-dimensional Turing machine with emergent behavior
this result was incorrectly attributed and is known as the Cohen-Kong theorem. In 2000, Gajardo et al. showed a construction that calculates any boolean
Langton's_ant
Carnot's theorem (conics) Carnot's theorem (inradius, circumradius) Carnot's theorem (perpendiculars) Catalogue of Triangle Cubics Centroid Ceva's theorem Cevian
List_of_triangle_topics
Theorem in geometric topology
conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere (the hypersphere that bounds
Poincaré_conjecture
Matthew Stewart publishes Some General Theorems of Considerable use in the Higher Parts of Mathematics, including an account of Stewart's theorem on the
1746_in_science
German polymath and scholar (1777–1855)
Gauss produced the second and third complete proofs of the fundamental theorem of algebra. He also introduced the triple bar symbol (≡) for congruence
Carl_Friedrich_Gauss
Infinite game in descriptive set theory whose payoff set is a lightface analytic set
existence of 0#, a result known as the Martin–Harrington theorem. The games studied here are Gale-Stewart games. Two players, conventionally called Player I
Lightface_analytic_game
developed the theories of rings, fields, and algebras. In physics, Noether's theorem explains the connection between symmetry and conservation laws. Enheduanna
List of women in the Heritage Floor
List_of_women_in_the_Heritage_Floor
The non-squeezing theorem, also called Gromov's non-squeezing theorem, is one of the most important theorems in symplectic geometry. It was first proven
Non-squeezing_theorem
Property of geometry, also used to generalize the notion of "distance" in metric spaces
Euclidean geometry and some other geometries, the triangle inequality is a theorem about vectors and vector lengths (norms): ‖ u + v ‖ ≤ ‖ u ‖ + ‖ v ‖ , {\displaystyle
Triangle_inequality
German mathematician (1882–1935)
contributions to abstract algebra. She also proved Noether's first and second theorems, which are fundamental in mathematical physics. Noether was described by
Emmy_Noether
Conjecture in number theory
smaller than c {\displaystyle c} . A number of famous conjectures and theorems in number theory would follow immediately from the abc conjecture or its
Abc_conjecture
Connects the homology of the symmetric groups with mapping spaces of spheres
symmetric groups and mapping spaces of spheres. The theorem (named after Michael Barratt, Stewart Priddy, and Daniel Quillen) is also often stated as
Barratt–Priddy_theorem
Economic model for international trade
Stolper–Samuelson theorem). The Magnification effect on production quantity-shifts induced by endowment changes (via the Rybczynski theorem) predicts a larger
Heckscher–Ohlin_model
Extends the Jordan curve theorem to characterize the inner and outer regions
the Schoenflies problem or Schoenflies theorem, of geometric topology is a sharpening of the Jordan curve theorem by Arthur Schoenflies. For Jordan curves
Schoenflies_problem
Award for quantum mechanics and their applications
Faculty of Arts and Science. Named after John Stewart Bell (the physicist behind Bell's theorem, a theorem whose experimental vindication led to a Nobel
John_Stewart_Bell_Prize
Matrix decomposition
n } {\displaystyle i>\min\{m,n\}} . The geometric content of the SVD theorem can thus be summarized as follows: for every linear map T : C n → C m
Singular_value_decomposition
Branch of mathematics
curves. These two branches are related to each other by the fundamental theorem of calculus. Calculus uses convergence of infinite sequences and infinite
Calculus
Bound on probability of a random variable being far from its mean
(the square root of the variance). The rule is often called Chebyshev's theorem, about the range of standard deviations around the mean, in statistics
Chebyshev's_inequality
First article on transfinite set theory
Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties. One of these theorems is his "revolutionary
Cantor's first set theory article
Cantor's_first_set_theory_article
Branch of mathematics
of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, a problem that was stated in terms of elementary arithmetic, and remained
Geometry
equations of mathematical physics. In 1896 he gave a proof of the prime number theorem that defines the frequency of prime numbers among the integers (also see
Meanings of minor-planet names: 10001–11000
Meanings_of_minor-planet_names:_10001–11000
Idea about population growth and food supply
methods determining population. Environmentalist founder of Ecomodernism, Stewart Brand, summarised how the Malthusian predictions of The Population Bomb
Malthusianism
1941 book
mathematics, including the proofs of the four-color map theorem and Fermat's last theorem, written by Ian Stewart. The book was based on Courant's course material
What_Is_Mathematics?
Morihiko Saito, 2001) Modularity theorem (Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor, 2001) Erdős–Stewart conjecture (Florian Luca, 2001)
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Type of construction
send the midpoint elsewhere. This is in contrast to the Mohr–Mascheroni theorem, which states that every straightedge and compass construction can be made
Straightedge-only construction
Straightedge-only_construction
Mathematical relation consisting of a multi-variable function equal to zero
Some equations do not admit an explicit solution. The implicit function theorem provides conditions under which some kinds of implicit equations define
Implicit_function
Universality of construction using just a straightedge and a single circle with center
In Euclidean geometry, the Poncelet–Steiner theorem is a result about compass and straightedge constructions with certain restrictions. This result states
Poncelet–Steiner_theorem
Type of vector space in math
Theorem 12.6 Reed & Simon 1980, p. 38 Young 1988, p. 23 Clarkson 1936 Rudin 1987, Theorem 4.10 Dunford & Schwartz 1958, II.4.29 Rudin 1987, Theorem 4
Hilbert_space
Brothers Grimm (2005), The Imaginarium of Doctor Parnassus (2009), The Zero Theorem (2013) John Gilling Sid James Escape by Night (1953), Interpol (1957),
List of film director and actor collaborations
List_of_film_director_and_actor_collaborations
Method of deriving conclusions
inferential steps and often use various rules of inference to establish the theorem they intend to demonstrate. Rules of inference are definitory rules—rules
Rule_of_inference
Limit type in multivariable calculus
m}-L\right|<\varepsilon } . The following theorem states the relationship between double limit and iterated limits. Theorem 1. If lim n → ∞ m → ∞ a n , m {\displaystyle
Iterated_limit
Field of knowledge
and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems
Mathematics
Characteristic property of holomorphic functions
{\partial (-v)}{\partial y}}=0.} Owing respectively to Green's theorem and the divergence theorem, such a field is necessarily a conservative one on any simply-connected
Cauchy–Riemann_equations
Subfield of mathematics
mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary
Mathematical_logic
Type of equation with integer coefficients
The most significant qualitative improvement to the theorem of Bombieri and Schmidt is due to Stewart, who obtained a bound of the form C ( f , r ) = C
Thue_equation
Pathological embedding of the sphere in 3D space
connected, unlike the exterior of the usual round sphere. The Schoenflies theorem in 2D states that any simple closed curve in the plane can be extended
Alexander_horned_sphere
Partition of a toroidal surface into polygons
all adjacent to each other, hence providing the existence half of the theorem that the maximum number of colors needed for a map on a (genus one) torus
Toroidal_polyhedron
In mathematics, with negligible exceptions
almost all elements of X, even if it isn't an ultrafilter. The prime number theorem shows that the number of primes less than or equal to n is asymptotically
Almost_all
2012 nonfiction book by mathematician Ian Stewart
the role of mathematics in human history, beginning with the Pythagorean theorem to the equation that transformed twenty-first century financial markets
In_Pursuit_of_the_Unknown
Point to which functions converge in analysis
advantages of working with non-deleted limits is that they allow to state the theorem about limits of compositions without any constraints on the functions (other
Limit_of_a_function
Concept in complex analysis
of potential functions for conservative vector fields, in that Green's theorem is only able to guarantee path independence when the function in question
Antiderivative (complex analysis)
Antiderivative_(complex_analysis)
Book by Ian Stewart
conjecture Squaring the circle Four colour theorem Kepler's conjecture Mordell's conjecture Fermat's Last Theorem Three-body problem Riemann hypothesis Poincare
The Great Mathematical Problems
The_Great_Mathematical_Problems
Type of clock
fractal sundial. The theorem was proved in 1987 by Kenneth Falconer. Four years later it was described in Scientific American by Ian Stewart. The first prototype
Digital_sundial
Mathematical model of financial markets
attached when they first unveiled the formula." British mathematician Ian Stewart, author of the 2012 book entitled In Pursuit of the Unknown: 17 Equations
Black–Scholes_model
American philosopher
Smullyan. The Limits of Logic: Higher-Order Logic and the Löwenheim-Skolem Theorem, Routledge, 1996. Special issue of Philosophia Mathematica 4(2), devoted
Stewart_Shapiro
now known as the Hajnal–Szemerédi theorem. A conjecture that would have strengthened the Furstenberg–Sárközy theorem to state that the number of elements
List of conjectures by Paul Erdős
List_of_conjectures_by_Paul_Erdős
Largest and smallest value taken by a function at a given point
function is continuous on a closed interval, then by the extreme value theorem, global maxima and minima exist. Furthermore, a global maximum (or minimum)
Maximum_and_minimum
Plane curve: conic section
m_{1}-m_{2}.} Analogous to the inscribed angle theorem for circles, one has the inscribed angle theorem for parabolas: Four points P i = ( x i , y i )
Parabola
Mathematical approximation of a function
function, which become generally more accurate as n increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such
Taylor_series
Field of mathematics and science based on non-linear systems and initial conditions
the system into two open sets. An important related theorem is the Birkhoff Transitivity Theorem. It is easy to see that the existence of a dense orbit
Chaos_theory
Set with associative invertible operation
particular p. 273 for concrete examples). Lang 2002, p. 292, (Theorem VI.7.2). Stewart 2015, §12.1. Kurzweil & Stellmacher 2004, p. 3. Artin 2018, Proposition
Group_(mathematics)
Shape with four equal sides and angles
number of equal-area triangles, a result of Monsky's theorem. Cross's theorem or Vecten's theorem states that, for a triangle formed by the sides of three
Square
Indefinite integral
Antiderivatives are related to definite integrals through the second fundamental theorem of calculus: the definite integral of a function over a closed interval
Antiderivative
Mix of funds used to start and sustain a business
amount of debt in a company's capital structure. The Miller and Modigliani theorem argues that the market value of a firm is unaffected by a change in its
Capital_structure
important for his work in pure mathematics, having authored a number of theorems. Frank Wilczek (born 1951): American theoretical physicist. Along with
List_of_agnostics
Number with a real and an imaginary part
that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real
Complex_number
Mathematical rule for evaluating limits
L'Hôpital's rule (/ˌloʊpiːˈtɑːl/ loh-pee-TAHL) is a mathematical theorem used for evaluating the limit of a quotient of two functions, each of which tends
L'Hôpital's_rule
Alternative decimal expansion of 1
(1976), p. 61, Theorem 3.26; Stewart (1999), p. 706. Euler (1828), p. 170. Grattan-Guinness (1970), p. 69; Bonnycastle (1806), p. 177. Stewart (1999), p. 706;
0.999...
Triangular array of the binomial coefficients
triangle (مثلث خیام-پاسکال). Several theorems related to the triangle were known, including the binomial theorem. Pascal's triangle was known in China
Pascal's_triangle
Class of theories in quantum mechanics
In quantum mechanics, superdeterminism is a loophole in Bell's theorem. By postulating that all systems being measured are correlated with the choices
Superdeterminism
functions, and sets. Mathematical objects can be very complex; for example, theorems, proofs, and even formal theories are considered as mathematical objects
Mathematical_object
Standard example in game theory
Abilene paradox Centipede game Collective action problem Externality Folk theorem (game theory) Free-rider problem Gift-exchange game Hobbesian trap Innocent
Prisoner's_dilemma
American voice actor (born 1962)
Episode: "Gone With the Wand" Transformers: Robots in Disguise Axiom and Theorem Episode: "Brainpower" New Looney Tunes Hubie and Bertie Episode: "Appropriate
Jeff_Bennett
Experiments to test Bell's theorem in quantum mechanics
stated the problem in the famous EPR paper. In 1964, John Stewart Bell proposed his famous theorem, which states that no physical theory of hidden local variables
Bell_test
Historical critique of quantum mechanics
local hidden-variable theory. This second result became known as the Bell theorem. To understand the first result, consider the following toy hidden-variable
Einstein–Podolsky–Rosen paradox
Einstein–Podolsky–Rosen_paradox
Algorithm for computing greatest common divisors
it can be used as a basic tool for proving theorems in number theory such as Lagrange's four-square theorem and the uniqueness of prime factorizations
Euclidean_algorithm
STEWARTS THEOREM
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