To infinity and beyond: a cultural history of the infinite 9780691025117, 0691025118, 1654170534, 1623170834

Table of contents :
Title ......Page 3
Copyright ......Page 4
Dedication ......Page 5
Preface ......Page 7
Contents ......Page 15
Part I. Mathematical Infinity ......Page 17
1. First Steps to Infinity ......Page 18
Zero, One, Infinity ......Page 22
2. Towards Legitimation ......Page 26
Numbers Large and Small ......Page 30
3. Convergence and Limit ......Page 33
The Prime Numbers ......Page 37
4. The Fascination of Infinite Series ......Page 41
5. The Geometric Series ......Page 45
6. More about Infinite Series ......Page 50
7. Interlude: An Excursion into the Number Concept ......Page 56
8. The Discovery of Irrational Numbers ......Page 60
A Do-It-Yourself Method for Finding √2 ......Page 65
π, ф, and e — Three Celebrated Irrationals ......Page 66
9. Cantor's New Look at the Infinite ......Page 70
10. Beyond Infinity ......Page 77
Part II. Geometric Infinity ......Page 83
11. Some Functions and Their Graphs ......Page 84
Some Geometric Paradoxes Involving Infinity ......Page 99
12. Inversion in a Circle ......Page 104
13. Geographic Maps and Infinity ......Page 111
14. Tiling the Plane ......Page 118
15. A New Look at Geometry ......Page 124
16. The Vain Search for Absolute Truth ......Page 134
Part III. Aesthetic Infinity ......Page 151
17. Rejoice the Infinite! ......Page 152
18. The Mobius Strip ......Page 155
19. The Magic World of Mirrors ......Page 165
20. Horror Vacui, Amor Infiniti ......Page 171
21. Maurits C. Escher—Master of the Infinite ......Page 180
22. The Modern Kabbalists ......Page 195
Part IV. Cosmological Infinity ......Page 199
23. The Ancient World ......Page 200
24. The New Cosmology ......Page 206
25. The Horizons Are Receding ......Page 215
26. A Paradox and Its Aftermath ......Page 220
27. The Expanding Universe ......Page 228
28. The Modern Atomists ......Page 240
29. Which Way from Here? ......Page 243
Epilogue ......Page 248
Appendix ......Page 251
Bibliography ......Page 276
Index ......Page 285