Introduction to Circle Packing

This book, first published in 2005, introduces a new mathematical topic known as 'circle packing', taking the reader from first definitions to late-breaking results.

This book introduces a new mathematical topic known as 'circle packing', taking the reader from first definitions to late-breaking results.

Autorentext
Kenneth Stephenson is Professor of Mathematics at the University of Tennessee in Knoxville, where he has established an active research program in complex function theory. He has had visiting positions at the University of Hawaii and Florida State University, and sabbatical appointments at the Open University and the University of Cambridge. Over the last fifteen years he has centered his research on circle packing. In this book he formulates circle packing as a discrete incarnation of classical analytic function theory.

Klappentext
This book introduces circle packing, a new mathematical topic with a wide audience and a bright future. The subject can be enjoyed for visual appeal, the elegance of circle geometry, the clean theory, classical connections, or for applications. The book shifts smoothly from intuitive notions to links with core areas of complex analysis and Riemann surfaces. However, it is firmly grounded in a computational, experimental and visual approach, which carries the reader from first definitions to late-breaking results and provides many enticing and accessible open problems.


Inhalt
Part I. An Overview of Circle Packing: 1. A circle packing menagerie; 2. Circle packings in the wild; Part II. Rigidity: Maximal Packings: 3. Preliminaries: topology, combinatorics, and geometry; 4. Statement of the fundamental result; 5. Bookkeeping and monodromy; 6. Proof for combinatorial closed discs; 7. Proof for combinatorial spheres; 8. Proof for combinatorial open discs; 9. Proof for combinatorial surfaces; Part III. Flexibility: Analytic Functions: 10. The intuitive landscape; 11. Discrete analytic functions; 12. Construction tools; 13. Discrete analytic functions on the disc; 14. Discrete entire functions; 15. Discrete rational functions; 16. Discrete analytic functions on Riemann surfaces; 17. Discrete conformal structure; 18. Random walks on circle packings; Part IV: 19. Thurston's Conjecture; 20. Extending the Rodin/Sullivan theorem; 21. Approximation of analytic functions; 22. Approximation of conformal structures; 23. Applications; Appendix A. Primer on classical complex analysis; Appendix B. The ring lemma; Appendix C. Doyle spirals; Appendix D. The brooks parameter; Appendix E. Schwarz and buckyballs; Appendix F. Inversive distance packings; Appendix G. Graph embedding; Appendix H. Square grid packings; Appendix I. Experimenting with circle packings.

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