Heiko Harborth raised the question of whether every planar graph has a straight line representation in which all edge lengths are integers.
For maximal planar graphs, in which every face is a triangle, a greedy planar embedding can be found by applying the Knaster–Kuratowski–Mazurkiewicz lemma to a weighted version of a straight-line embedding algorithm of Schnyder.
Liouville's theorem | Chinese remainder theorem | Shannon–Hartley theorem | Quillen–Suslin theorem | Nyquist–Shannon sampling theorem | Hahn–Banach theorem | Fermat's Last Theorem | El Fary | Buckingham π theorem | Thue–Siegel–Roth theorem | Szemerédi's theorem | Schottky's theorem | Riemann-Roch theorem | Pythagorean theorem | Nash embedding theorem | Müntz–Szász theorem | Malgrange–Ehrenpreis theorem | Kleene fixed-point theorem | Kakutani fixed-point theorem | Gauss–Bonnet theorem | Doob's martingale convergence theorem | Dirichlet's theorem on arithmetic progressions | Denjoy theorem | Birch's theorem | Wilkie's theorem | Wick's theorem | Whitney extension theorem | Weierstrass theorem | Wedderburn's little theorem | Vietoris–Begle mapping theorem |
Both appeared, alongside several other important theorems, in a well-known paper by József Beck.
For the theorem named after Felix Bloch on wave functions of a particle in a periodic potential, see Bloch wave.
But it was proven much earlier by Yusuf Al-Mu'taman ibn Hűd, an eleventh-century king of Zaragoza.
Because this constraint is nonholonomic, Liouville's theorem does not apply, and although energy is conserved, the motion is dissipative in the sense that phase space volume is not conserved.
Chow–Rashevskii theorem: In sub-Riemannian geometry, the theorem that asserts that any two points are connected by a horizontal curve.
The constant is irrational; this can be proven with Dirichlet's theorem on arithmetic progressions or Bertrand's postulate (Hardy and Wright, p. 113) or Ramare's theorem that every even integer is a sum of at most six primes.
In a 1969 paper, Dutch mathematician Nicolaas Govert de Bruijn proved several results about packing congruent rectangular bricks (of any dimension) into larger rectangular boxes, in such a way that no space is left over.
Emile Bachelet applied Earnshaw's theorem and the Braunbeck extension and stabilized magnetic force by controlling current intensity and turning on and off power to the electromagnets at desired frequencies.
Ajtai and Szemerédi proved the corners theorem, an important step toward higher dimensional generalizations of the Szemerédi theorem.
The works of 17th century mathematician Pierre de Fermat engendered many theorems.
Friedrich Hermann Schottky (24 July 1851 – 12 August 1935) was a German mathematician who worked on elliptic, abelian, and theta functions and introduced Schottky groups and Schottky's theorem.
According to Euler's theorem these 12 pentagons are required for closure of the carbon network consisting of n hexagons and C60 is the first stable fullerene because it is the smallest possible to obey this rule.
Professor Sergei K. Godunov originally proved the theorem as a Ph.D. student at Moscow State University.
While gravitational lensing preserves surface brightness, as dictated by Liouville's theorem, lensing does change the apparent solid angle of a source.
Cousin's theorem states that for every gauge , such a -fine partition P does exist, so this condition cannot be satisfied vacuously.
Hilbert's basis theorem, in commutative algebra, stating every ideal in the ring of multivariate polynomials over a Noetherian ring is finitely generated
•
Hilbert's irreducibility theorem, in number theory, concerning irreducible polynomials
•
Hilbert's syzygy theorem, a result of commutative algebra in connection with the syzygy problem of invariant theory
•
Hilbert's Theorem 90, an important result on cyclic extensions of fields that leads to Kummer theory
•
Hilbert's Nullstellensatz, the basis of abstract algebra, establishing a fundamental relationship between geometry and algebra
He has also done art for Lasers Dragons and Lies with John Zakour and Intergalactic Law: Grey Squad with Lisa Fary on Zuda as well as Intergalactic Law on Pink Raygun where he is the art director.
Kellogg's theorem is a pair of related results in the mathematical study of the regularity of harmonic functions on sufficiently smooth domains by Oliver Dimon Kellogg.
Cayley's formula follows from Kirchhoff's theorem as a special case, since every vector with 1 in one place, −1 in another place, and 0 elsewhere is an eigenvector of the Laplacian matrix of the complete graph, with the corresponding eigenvalue being n.
This result may also be known as the Kolmogorov theorem; see Kolmogorov's theorem for disambiguation.
Kōmura's theorem, result on the differentiability of absolutely continuous Banach space-valued functions
The following lemma is usually known as Liouville's theorem (on diophantine approximation), there being several results known as Liouville's theorem.
For example, the first version of Montel's theorem stated above is the analog of Liouville's theorem, while the second version corresponds to Picard's theorem.
Morley's categoricity theorem, a theorem related to model theory, discovered by Michael D. Morley
•
Morley's trisector theorem, a theorem related to geometry, discovered by Frank Morley
Between 1999 and 2004, David Laibman, a Marxist economist, published at least nine pieces dealing with the Temporal single-system interpretation (TSSI) of Marx's value theory.
In the 1990s, Alex Wilkie showed that one has the same result if instead of adding every analytic function, one just adds the exponential function to R to get the ordered real field with exponentiation, Rexp, a result known as Wilkie's theorem.
Poynting's theorem on conservation of energy in electromagnetic field
Then, for any sets U and V, by the Chinese remainder theorem, the numbers that are quadratic resides modulo every prime in U and nonresidues modulo every prime in V form a periodic sequence, so by Dirichlet's theorem on primes in arithmetic progressions this number-theoretic graph has the extension property.
The Reflections contain a number of principles such as the Carnot cycle, the Carnot heat engine, Carnot's theorem, thermodynamic efficiency.
Brauer's theorem on the representability of zero by forms over certain fields in sufficiently many variables
The theorem for compact Riemann surfaces can be deduced from the algebraic version using Chow's theorem and the GAGA principle: in fact, every compact Riemann surface is defined by algebraic equations in some complex projective space.
Theodor Estermann (1902–1991) proved in his book Complex Numbers and Functions the following relation: Let be a bounded region with continuous boundary .
In computational complexity theory, Savitch's theorem, proved by Walter Savitch in 1970, gives a relationship between deterministic and non-deterministic space complexity.
Schaefer's dichotomy theorem, a theorem about the theory of NP-completeness by Thomas J. Schaefer
Stagnation zones theorems are closely related to pre-Liouville's theorems about evaluation of solutions fluctuation, which direct consequences are the different versions of the classic Liouville theorem about conversion of the entire doubly periodic function into the identical constant.
Syamadas Mukhopadhyaya (June 22, 1866 – May 8, 1937) was an Indian mathematician who introduced the four-vertex theorem and Mukhopadhyaya's theorem in plane geometry.
An earlier version of the result is already mentioned in 1671 by James Gregory.
The theorem was independently derived in 1853 by the German scientist Hermann von Helmholtz and in 1883 by Léon Charles Thévenin (1857–1926), an electrical engineer with France's national Postes et Télégraphes telecommunications organization.
Thue–Siegel–Roth theorem, also known as Roth's theorem, is a foundational result in diophantine approximation to algebraic numbers.
1930s: British mathematician Mary Cartwright proved her theorem, now known as Cartwright's theorem, which gives an estimate for the maximum modulus of an analytic function that takes the same value no more than p times in the unit disc.
The prototype of such results is Turán's theorem, where there is one forbidden subgraph: a complete graph with k vertices (k is fixed).
Thesis "Vincent's Theorem in Algebraic Manipulation", North Carolina State University, USA, 1978.
The solution to Waring's problem for cubes, that every integer is the sum of at most 9 cubes