To Infinity and Beyond: A Cultural History of the Infinite

To Infinity and Beyond: A Cultural History of the Infinite

Book rating: 05 Paperback Princeton Paperbacks

By (author) Eli Maor

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  • Publisher: Princeton University Press
  • Format: Paperback | 296 pages
  • Dimensions: 163mm x 236mm x 15mm | 476g
  • Publication date: 29 July 1991
  • Publication City/Country: New Jersey
  • ISBN 10: 0691025118
  • ISBN 13: 9780691025117
  • Illustrations note: Ill.
  • Sales rank: 211,717

Product description

In this title, 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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Customer reviews

By L. Dane Gray 28 Oct 2011 5

This book is an amazing read which doesnt really require much knowledge of mathematics but can still take you deep into its philosophical theories.

Review quote

"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 "Fascinating and enjoyable ... [P]laces the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."--Science

Back cover copy

'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

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 Mobius 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