To Infinity and Beyond: A Cultural History of the Infinite

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Princeton University Press, 1991 - Mathematics - 284 pages
9 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

  

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Review: To Infinity and Beyond: A Cultural History of the Infinite

User Review  - Ann - Goodreads

This book is a bit of a challenge if you are rusty of math but Maor does a good job of presenting the material with interesting footnotes (mostly historical in nature) and proofs in the appendix. He ... Read full review

Review: To Infinity and Beyond: A Cultural History of the Infinite

User Review  - Zac - Goodreads

a decently written book that still holds MOSTLY true considering it was written in 1987. good concepts, well explained. Read full review

Contents

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 Number
21
4 The Fascination of Infinite Series
25
5 The Geometric Series
29
16 The Vain Search for Absolute Truth
118
Aesthetic Infinity
135
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

6 More about Infinite Series
34
An Excursion into the Number Concept
40
8 The Discovery of Irrational Numbers
44
A DoItYourself Method for Finding 2
49
𝜋 𝜙 and eThree Celebrated Irrationals
50
9 Cantors New Look at the Infinite
54
10 Beyond Infinity
61
Geometric Infinity
67
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
Cosmological Infinity
183
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
Copyright

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About the author (1991)

Eli Maor is a teacher of the history of mathematics who has successfully popularized his subject with the general public through a series of informative and entertaining books. In "E: The Story of a Number," Maor uses anecdotes, excursions and essays to illustrate that number's importance to mathematics. "Trigonometric Delights" brings trigonometry to life by blending history, biography, scientific curiosities and mathematics to achieve the goal of showing how trigonometry has contributed to both science and social development. "To Infinity and Beyond: A Cultural History of the Infinite" explores the idea of infinity in mathematics and art through the use of the illustrations of the Dutch artist M.C. Escher. Eli Maor's readable books have made the world of numbers accessible even to those with little or no background in mathematics.

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