Plato, Poincaré, and the Enchanted Dodecahedron: Is the Universe Shaped Like the Poincaré Homology Sphere?

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Introduction ix
4. Mathematics and the Good Life 1
5. The Rise of Big Data: How It’s Changing the Way We Think about the World 20
6. Conway’s Wizards 33
7. On Unsettleable Arithmetical Problems 39
8. Crinkly Curves 49
9. Why Do We Perceive Logarithmically? 64
10. The Music of Math Games 74
11. The Fundamental Theorem of Algebra for Artists 87
12. The Arts—Digitized, Quantified, and Analyzed 96
13. On the Number of Klein Bottle Types 105
14. Adventures in Mathematical Knitting 128
15. The Mathematics of Fountain Design: A Multiple-Centers Activity 144
16. Food for (Mathematical) Thought 156
17. Wondering about Wonder in Mathematics 165
18. The Lesson of Grace in Teaching 188
19. Generic Proving: Reflections on Scope and Method 198
20. Extreme Proofs I: The Irrationality of √2 216
21. Stuck in the Middle: Cauchy’s Intermediate Value Theorem and the History of Analytic Rigor 228
22. Plato, Poincaré, and the Enchanted Dodecahedron: Is the Universe Shaped Like the Poincaré Homology Sphere? 239
23. Computing with Real Numbers, from Archimedes to Turing and Beyond 251
24. Chaos at Fifty 270
25. Twenty-Five Analogies for Explaining Statistical Concepts 288
26. College Admissions and the Stability of Marriage 299
27. The Beauty of Bounded Gaps 308
28. Contributors 315
29. Notable Writings 325
30. Acknowledgments 333
31. Credits 335