To Infinity and Beyond

A Cultural History of the Infinite - New Edition

Eli Maor (Autor)

Buch | Softcover

304 Seiten

2017 | Revised edition
Princeton University Press (Verlag)
978-0-691-17811-0 (ISBN)

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To Infinity and Beyond explores the idea of infinity in mathematics and art. Eli Maor examines the role of infinity, as well as 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.

Eli Maor is the author of Beautiful Geometry (with Eugen Jost), Venus in Transit, Trigonometric Delights, e: The Story of a Number, and The Pythagorean Theorem: A 4,000-Year History (all Princeton).

Foreword vii

Preface i

Color Insert 43

Part I Mathematical Infinity

1 First Steps to Infinity 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 //2 49

Pi, Phi, and e--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 Circle 88

13 Geographic Maps and Infinity 95

14 Tiling the Plane 102

15 New Look at Geometry 108

16 The Vain Search for Absolute Truth 118

Part III Aesthetic Infinity

17 Rejoice the Infinite! 136

18 The Mobius Scrip 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 19

Part IV Cosmological Infinity

23 The Ancient World 184

24 The New Cosmology 190

25 The Horizons Are Receding 199

26 Paradox and Its Aftermath 204

27 The Expanding Universe 212

28 The Modern Atomises 224

29 Which Way from Here? 227

Epilogue 232

Appendix 235

Bibliography 260

Index 269

Erscheinungsdatum	05.12.2017
Reihe/Serie	Princeton Science Library
Vorwort	Ian Stewart
Zusatzinfo	6 page color insert
Verlagsort	New Jersey
Sprache	englisch
Maße	140 x 216 mm
Gewicht	510 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
	Naturwissenschaften
ISBN-10	0-691-17811-9 / 0691178119
ISBN-13	978-0-691-17811-0 / 9780691178110
Zustand	Neuware