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Matousek J. Introduction to Discrete Geometry 2003
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Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object.
Department of Applied Mathematics.
Convexity
Linear and Affine Subspaces, General Position
Convex Sets, Convex Combinations, Separation
Radon’s Lemma and Helly’s Theorem
Centerpoint and Ham Sandwich
Lattices and Minkowski’s Theorem
Minkowski’s Theorem
General Lattices
An Application in Number Theory
Convex Independent Subsets
The Erdős–Szekeres Theore
Horton Sets
Incidence Problems
Formulation
Lower Bounds: Incidences and Unit Distance
Point–Line Incidences via Crossing Numbers
Convex Polytopes
Geometric Duality
H-Polytopes and V -Polytopes
Faces of a Convex Polytope
Many Faces: The Cyclic Polytopes
The Upper Bound Theorem
Voronoi Diagrams
Number of Faces in Arrangements
Arrangements of Hyperplanes
Arrangements of Other Geometric Objects
Number of Vertices of Level at Most k
The Zone Theore

Matousek J. Introduction to Discrete Geometry 2003.pdf3.83 MiB