Synopses & Reviews
Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement. "Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates."--Los Angeles Times "[Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama."--Choice "Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."--Science
Synopsis
Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement. "Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates."--Los Angeles Times "[Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama."--Choice "Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."--Science
Description
Includes bibliographical references (p. 260-267) and index.
Table of Contents
Preface vii
Color Plates 143
Part I. Mathematical Infinity
1. First Steps to Infinity 2
Zero, One, Infinity 6
2. Towards Legitimation 10
Numbers Large and Small 14
3. Convergence and Limit 17
The Prime Numbers 21
4. The Fascination of Infinite Series 25
5. The Geometric Series 29
6. More about Infinite Series 34
7. Interlude: An Excursion into the Number Concept 40
8. The Discovery of Irrational Numbers 44
A Do-It-Yourself Method for Finding [Square Root of] 2 49
Three Celebrated Irrationals 50
9. Cantor's New Look at the Infinite 54
10. Beyond Infinity 61
Part II. Geometric Infinity
11. Some Functions and Their Graphs 68
Some Geometric Paradoxes Involving Infinity 83
12. Inversion in a Circle 88
13. Geographic Maps and Infinity 95
14. Tiling the Plane 102
15. A New Look at Geometry 108
16. The Vain Search for Absolute Truth 118
Part III. Aesthetic Infinity
17. Rejoice the Infinite! 136
18. The Möbius Strip 139
19. The Magic World of Mirrors 149
20. Horror Vacui, Amor Infiniti 155
21. Maurits C. Escher--Master of the Infinite 164
22. The Modern Kabbalists 179
Part IV. Cosmological Infinity
23. The Ancient World 184
24. The New Cosmology 190
25. The Horizons Are Receding 199
26. A Paradox and Its Aftermath 204
27. The Expanding Universe 212
28. The Modern Atomists 224
29. Which Way from Here? 227
Epilogue 232
Appendix 235
Bibliography 260
Index 269