Category
page 1Theorems in discrete geometry
Sylvester–Gallai theorem
theorem that every finite set of points in the plane, not all collinear, has a line through exactly two points
Wallace–Bolyai–Gerwien theorem
theorem
Erdős–Szekeres theorem
theorem that sufficiently long sequences of numbers have long monotonic subsequences
Krein–Milman theorem
theorem
Cauchy's theorem
theorem in geometry
Radon's theorem
theorem that d+2 points in d dimensions can be partitioned into two subsets whose convex hulls intersect
four-vertex theorem
theorem that every simple closed smooth curve in the plane has at least four points of locally extreme curvature
Helly's theorem
theorem about the intersections of d-dimensional convex sets
De Bruijn–Erdős theorem
incidence geometry theorem
Szemerédi–Trotter theorem
bound on the number of incidences between points and lines in the plane
Carathéodory's theorem
theorem on convex hulls
Balinski's theorem
mathematical theorem concerning the graph-theoretic structure of three-dimensional polyhedra and higher-dimensional polytopes
Monsky's theorem
One can't dissect a square into an odd number of triangles of equal area
Erdős–Anning theorem
infinite set of points in R2 with mutual integer distances must be a straight line
Tverberg's theorem
theorem in discrete geometry
Steinitz's theorem
Characterizes graphs formed by edges and vertices of 3-dimensional convex polyhedra
Alexandrov's uniqueness theorem
rigidity theorem in mathematics