Discrete geometry investigates combinatorial properties of configurations ofgeometric objects. To a working mathematician or computer scientist it offerssophist... » 

Discrete geometry investigates combinatorial properties of configurations ofgeometric objects. To a working mathematician or computer scientist it offerssophisticated results and techniques of great diversity and it is a foundationfor fields such as computational geometry or combinatorial optimization.BRThisbook is primarily a textbook introduction to various areas of discretegeometry. In each area it explains several key results and methods in anaccessible and concrete manner. It also contains more advanced material inseparate sections and thus it can serve as a collection of surveys in severalnarrower subfields. The main topics include basics on convex sets convexpolytopes and hyperplane arrangements combinatorial complexity of geometricconfigurations intersection patterns and transversals of convex setsgeometric Ramseytype results polyhedral combinatorics and highdimensionalconvexity and lastly embeddings of finite metric spaces into normedspaces.BRJiri Matousek is Professor of Computer Science at Charles Universityin Prague. His research has contributed to several of the considered areas andto their algorithmic applications. This is his third book. TOCPreface.Notation and Terminology. Convexity. Lattices and Minkowskis Theorem.Convex Independent Subsets. Incidence Problems. Convex Polytopes. Number ofFaces in Arrangements. Lower Envelopes. More Theorems in Convexity.Geometric Selection Theorems. Transversals and EpsilonNets. Attempts toCount ksets. Two Applications of HighDimensional Polytopes. Volumes in HighDimension. Measure Concentration and Almost Spherical Sections. EmbeddingFinite Metric Spaces into Normed Spaces. What Was It About An InformalSummary. Bibliography. Index. «