- Fields of mathematics
- >
- Discrete mathematics
- >
- Discrete geometry
- >
- Theorems in discrete geometry

- Fields of mathematics
- >
- Discrete mathematics
- >
- Theorems in discrete mathematics
- >
- Theorems in discrete geometry

- Fields of mathematics
- >
- Geometry
- >
- Theorems in geometry
- >
- Theorems in discrete geometry

- Geometry
- >
- Fields of geometry
- >
- Discrete geometry
- >
- Theorems in discrete geometry

- Mathematical problems
- >
- Mathematical theorems
- >
- Theorems in discrete mathematics
- >
- Theorems in discrete geometry

- Mathematical problems
- >
- Mathematical theorems
- >
- Theorems in geometry
- >
- Theorems in discrete geometry

- Mathematics
- >
- Mathematical theorems
- >
- Theorems in discrete mathematics
- >
- Theorems in discrete geometry

- Mathematics
- >
- Mathematical theorems
- >
- Theorems in geometry
- >
- Theorems in discrete geometry

- Theorems
- >
- Mathematical theorems
- >
- Theorems in discrete mathematics
- >
- Theorems in discrete geometry

- Theorems
- >
- Mathematical theorems
- >
- Theorems in geometry
- >
- Theorems in discrete geometry

De Bruijn–Erdős theorem (incidence geometry)

In incidence geometry, the De Bruijn–Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős, states a lower bound on the number of lines determined by n points in a projective

Erdős–Nagy theorem

The Erdős–Nagy theorem is a result in discrete geometry stating that a non-convex simple polygon can be made into a convex polygon by a finite sequence of flips. The flips are defined by taking a conv

Sylvester–Gallai theorem

The Sylvester–Gallai theorem in geometry states that every finite set of points in the Euclidean plane has a line that passes through exactly two of the points or a line that passes through all of the

Szemerédi–Trotter theorem

The Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given n points and m lines in the Euclidean plane, the number of incidences (i.e., the number

Erdős–Anning theorem

The Erdős–Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line. It is named after Paul Erdős and Norman

Erdős–Szekeres theorem

In mathematics, the Erdős–Szekeres theorem asserts that, given r, s, any sequence of distinct real numbers with length at least (r − 1)(s − 1) + 1 contains a monotonically increasing subsequence of le

Wallace–Bolyai–Gerwien theorem

In geometry, the Wallace–Bolyai–Gerwien theorem, named after William Wallace, Farkas Bolyai and , is a theorem related to dissections of polygons. It answers the question when one polygon can be forme

Kirchberger's theorem

Kirchberger's theorem is a theorem in discrete geometry, on linear separability. The two-dimensional version of the theorem states that, if a finite set of red and blue points in the Euclidean plane h

Carathéodory's theorem (convex hull)

Carathéodory's theorem is a theorem in convex geometry. It states that if a point x of Rd lies in the convex hull of a set P, then x can be written as the convex combination of at most d + 1 points in

Alexandrov's uniqueness theorem

The Alexandrov uniqueness theorem is a rigidity theorem in mathematics, describing three-dimensional convex polyhedra in terms of the distances between points on their surfaces. It implies that convex

Monsky's theorem

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 does not have an odd equidissection. The proble

Balinski's theorem

In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional convex polyhedra and higher-dimensional convex polytope

Helly's theorem

Helly's theorem is a basic result in discrete geometry on the intersection of convex sets. It was discovered by Eduard Helly in 1913, but not published by him until 1923, by which time alternative pro

Steinitz's theorem

In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are

Four-vertex theorem

The four-vertex theorem of geometry states that the curvature along a simple, closed, smooth plane curve has at least four local extrema (specifically, at least two local maxima and at least two local

Krein–Milman theorem

In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector spaces (TVSs). Krein–Milman theorem — A comp

Tverberg's theorem

In discrete geometry, Tverberg's theorem, first stated by Helge Tverberg, is the result that sufficiently many points in d-dimensional Euclidean space can be partitioned into subsets with intersecting

Beck's theorem (geometry)

In discrete geometry, Beck's theorem is any of several different results, two of which are given below. Both appeared, alongside several other important theorems, in a well-known paper by József Beck.

Radon's theorem

In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that any set of d + 2 points in Rd can be partitioned into two sets whose convex hulls intersect. A point in the

De Bruijn's theorem

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

Cauchy's theorem (geometry)

Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding faces must be congruent to each other. That is,

© 2023 Useful Links.