New Approaches to Circle Packing in a Square: With Program Codes

 Preface.- Glossary of Symbols.- 1. Introduction and Problem History.- 2. Problem Definitions and Formulations.- 3. Bounds for the Optimum Values.- 4. Approximate Circle Packings Using Optimization Methods.- 5. Other Methods for Finding Approximate Circle Packings.- 6. Interval Methods for Validating Optimal Solutions.- 7. The First Fully Interval-based Optimization Method.- 8. The Improved Version of the Interval Optimization Method.- 9. Interval Methods for Verifying Structural Optimality.- 10. Repeated Patterns in Circle Packings.- 11. Minimal Polynomials of Point Arrangements.- 12. About the Codes Used.- Appendix A. Currently Best Known Results for Packing Congruent Circles in a Square.- Bibliography.- Related Web Sites.- List of Figures.- List of Tables.- Index.