In arithmetic combinatorics, the corners theorem states that for every ε > 0 {\displaystyle \varepsilon >0} , for large enough N {\displaystyle N} , any...

have one corner that correspond to consecutive corners of the square. In this way they also form two boxes, this time in consecutive corners, with areas...

groups, rings and fields. Additive number theory Approximate group Corners theorem Ergodic Ramsey theory Problems involving arithmetic progressions Schnirelmann...

angles by which the smooth portions turn at the corners of the boundary. Many standard proofs use the theorem of turning tangents, which states roughly that...

circle theorem (Euclidean plane geometry) Cook's theorem (computational complexity theory) Corners theorem (arithmetic combinatorics) Corona theorem (complex...

Euclidean distances from P to two opposite corners of the rectangle equals the sum to the other two opposite corners. As an equation: A P 2 + C P 2 = B P 2...

_{2}^{2}(\triangle ABO),} which is de Gua's theorem. The generalisation of de Gua's theorem to n-simplices with right-angle corners can also be obtained as a special...

and Szemerédi proved the corners theorem, an important step toward higher-dimensional generalizations of the Szemerédi theorem. With Ajtai and János Komlós...

generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about...

developed a new proof of the density Hales–Jewett theorem based on ideas from the proof of the corners theorem. Dodos, Kanellopoulos, and Tyros gave a simplified...

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...

convex polygonal region occur at the region's corners. Further, if an extreme value occurs at two corners, then it must also occur everywhere on the line...

and Szemerédi proved the corners theorem, an important step toward higher-dimensional generalizations of the Szemerédi theorem. With Komlós and Szemerédi...

In mathematics, Lebesgue's density theorem states that for any Lebesgue measurable set A ⊂ R n {\displaystyle A\subset \mathbb {R} ^{n}} , the "density"...

The Zero Theorem is a 2013 science fiction film directed by Terry Gilliam, starring Christoph Waltz, David Thewlis, Mélanie Thierry and Lucas Hedges....

There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information...

In geometry, the Japanese theorem states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle...

diagonals, and tangent to the corners of the rectangle of incenters, the quadrilateral case of the cyclic polygon theorem can be proved in a few steps...

strong form of the exterior angle theorem and "Euclid's exterior angle theorem" as the weak form. A triangle has three corners, called vertices. The sides of...

Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem — A compact convex...

such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of...

standard 8×8 chessboard (or checkerboard) has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size...

In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}...

x_{i}+\Delta y_{i}=\Delta x_{i}+|f(x_{i})-f(x_{i-1})|.} By the mean value theorem, there exists some point x i ∗ {\displaystyle x_{i}^{*}} between x i {\displaystyle...

Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle...

impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program P computing a...

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...

In matrix theory, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive...

characteristic was originally defined for polyhedra and used to prove various theorems about them, including the classification of the Platonic solids. It was...

atoms (e.g. hydrogens) are at four corners of the cube (A, B, C, D) chosen so that no two atoms are at adjacent corners linked by only one cube edge. If...