Description
Book SynopsisA complete, self-contained introduction to a powerful and resurging mathematical discipline. Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Toth, Rogers, and Erd???s.
Table of ContentsARRANGEMENTS OF CONVEX SETS.
Geometry of Numbers.
Approximation of a Convex Set by Polygons.
Packing and Covering with Congruent Convex Discs.
Lattice Packing and Lattice Covering.
The Method of Cell Decomposition.
Methods of Blichfeldt and Rogers.
Efficient Random Arrangements.
Circle Packings and Planar Graphs.
ARRANGEMENTS OF POINTS AND LINES.
Extremal Graph Theory.
Repeated Distances in Space.
Arrangement of Lines.
Applications of the Bounds on Incidences.
More on Repeated Distances.
Geometric Graphs.
Epsilon Nets and Transversals of Hypergraphs.
Geometric Discrepancy.
Hints to Exercises.
Bibliography.
Indexes.
