CONTENTS
Polygonal
The Reidemeister approach to knot theory 235
There are true knots 238
Some families of knots 244
Chapter 18. On Soap Bubbles
Dirk Ferus 251
References and picture credits 259
Chapter 19.
and the Poincar´ e Conjecture
Klaus Ecker 261
1. Introduction 261
2. Geometry and topology of surfaces 263
3. Geometry and topology of three-dimensional spaces 276
4. Heat diffusion and the geometry of curves 285
5. Ricci flow, geometrization and the Poincar´ e Conjecture 288
6. Conclusion 296
References 296
Chapter 20. Chance and Mathematics: a Late Love
Ehrhard Behrends 299
1. How did it start? 299
2. How is it done today? 300
3. Fundamental concepts 302
4. Games of chance 305
5. Randomness vanishes at infinity 307
6. The productive role of chance 309
7. Chance in the microcosmos 310
8. Philosophical 312
Part 5. Epilogue 315
Chapter 21.
in a Multi-Media Civilization
Philip J. Davis 317
Poincar´ e’s predictions 318
What will pull mathematics into the future? 318
The inner texture (or soul) of mathematics 324
A personal illumination 329
References 330
The Prospects for Mathematics
ix
knots
Heat Diffusion, the Structure of Space,
Previous Page Next Page