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1 Hawthorne Mathematics- General

This title in other editions

To Infinity and Beyond: A Cultural History of the Infinite (Princeton Paperbacks)

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To Infinity and Beyond: A Cultural History of the Infinite (Princeton Paperbacks) Cover

 

Synopses & Reviews

Publisher Comments:

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

Product Details

ISBN:
9780691025117
Subtitle:
A Cultural History of the Infinite
Author:
Maor, Eli
Publisher:
Princeton University Press
Location:
Princeton, N.J. :
Subject:
General
Subject:
Logic
Subject:
History, criticism and surveys
Subject:
Infinite
Subject:
History -- Philosophy.
Subject:
History
Subject:
History of Science and Medicine, Philosophy of Science
Subject:
Mathematics
Subject:
Mathematics-Logic and Philosophy
Copyright:
Edition Description:
Trade paper
Series:
Princeton Paperbacks
Series Volume:
1975:1
Publication Date:
July 1991
Binding:
Paperback
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
296
Dimensions:
9.57x6.34x.65 in. 1.02 lbs.

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Related Subjects

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Humanities » Philosophy » General
Reference » Science Reference » Philosophy of Science
Science and Mathematics » Mathematics » Foundations and Logic
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To Infinity and Beyond: A Cultural History of the Infinite (Princeton Paperbacks) Used Trade Paper
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Product details 296 pages Princeton University Press - English 9780691025117 Reviews:
"Synopsis" by , 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
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