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

393 92 15MB

English Pages 301 Year 1991

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

Author / Uploaded
Maor E

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

Polecaj historie

To Infinity and Beyond 9781426223303, 9781426223600

This enlightening illustrated narrative by the world’s most celebrated astrophysicist explains the universe from the sol

144 55 49MB Read more

Beyond Infinity

Emotions are powerful. In newspaper headlines, on social media and in political debates, they have become the primary wa

860 68 12MB Read more

The Belle Époque: A Cultural History, Paris and Beyond 9780231554381

The years before the First World War have long been romanticized as a zenith of French culture—the “Belle Époque.” Domin

164 33 2MB Read more

Infinity and the Mind: The Science and Philosophy of the Infinite 9780691191256

A dynamic exploration of infinity In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the univ

163 18 23MB Read more

Infinity and the Mind: The Science and Philosophy of the Infinite [Course Book ed.] 9781400849048

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape,&q

210 69 27MB Read more

Metaphysics of Infinity: The Problem of Motion and the Infinite Brain 0761861475, 9780761861478

Since the time of the Greek philosopher Zeno (fifth century BCE), our faculty of analytic understanding has failed to co

179 27 2MB Read more

Critical Junctions: Anthropology and History beyond the Cultural Turn 9781782389620

The “cultural turn” has been a multifarious and pervasive phenomenon in Western universities and modes of social knowled

195 53 1012KB Read more

Achieving Infinite Resolution_A Gentle Look at the Role of Infinity in Calculus 9798656169677

243 25 16MB Read more

Infinite series in a history of analysis : stages up to the verge of summability 311034372X, 9783110343724

Higher mathematics once pointed towards the involvement of infinity. This we label analysis. The ancient Greeks had help

738 59 1MB Read more

Infinite Series in a History of Analysis: Stages up to the Verge of Summability 9783110359831, 9783110343724

"Higher mathematics" once pointed towards the involvement of infinity. This we label analysis. The ancient Gre

178 40 1MB Read more