Packing and Covering [Paperback]

Professor Rogers has written a economical and logical exposition of the theory of packing and covering.Professor Rogers has written this economical and logical exposition of the theory of packing and covering at a time when the simplest general results are known and future progress seems likely to depend on detailed and complicated technical developments.Professor Rogers has written this economical and logical exposition of the theory of packing and covering at a time when the simplest general results are known and future progress seems likely to depend on detailed and complicated technical developments.Professor Rogers has written this economical and logical exposition of the theory of packing and covering at a time when the simplest general results are known and future progress seems likely to depend on detailed and complicated technical developments. The book treats mainly problems in n-dimensional space, where n is larger than 3. The approach is quantative and many estimates for packing and covering densities are obtained. The introduction gives a historical outline of the subject, stating results without proof, and the succeeding chapters contain a systematic account of the general results and their derivation. Some of the results have immediate applications in the theory of numbers, in analysis and in other branches of mathematics, while the quantative approach may well prove to be of increasing importance for further developments.Introduction; 1. Packaging and covering densities; 2. The existence of reasonably dense packings; 3. The existence of reasonably economical coverings; 4. The existence of reasonably dense lattice packings; 5. The existence of reasonably economical lattice coverings; 6. Packings of simplices cannot be very dense; 8. Coverings with spheres cannot be very economical; Bibliography; Index.