Combinatorial geometry

Includes index.

Includes bibliographical references (p. 319-341)

I. Arrangements of Convex Sets. 1. Geometry of Numbers. 2. Approximation of a Convex Set by Polygons. 3. Packing and Covering with Congruent Convex Discs. 4. Lattice Packing and Lattice Covering. 5. The Method of Cell Decomposition. 6. Methods of Blichfeldt and Rogers. 7. Efficient Random Arrangements. 8. Circle Packings and Planar Graphs
Pt. II. Arrangements of Points and Lines. 9. External Graph Theory. 10. Repeated Distances in Space. 11. Arrangement of Lines. 12. Applications of the Bounds on Incidences. 13. More on Repeated Distances. 14. Geometric Graphs. 15. Epsilon Nets and Transversals of Hypergraphs. 16. Geometric Discrepancy

How many objects of a given shape and size can be packed into a large box of fixed volume? Can one plant n trees in an orchard, not all along the same line, so that every line determined by two trees will pass through a third? These questions, raised by Hilbert and Sylvester roughly one hundred years ago, have generated a lot of interest among professional and amateur mathematicians and scientists. They have led to the birth of a new mathematical discipline with close ties to classical geometry and number theory, and with many applications in coding theory, potential theory, computational geometry, computer graphics, robotics, etc.