To Infinity and Beyond: A Cultural History of the InfiniteEli 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 mindfrom 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 infinitya 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  GoodreadsThis 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  Goodreadsa 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 
260  
269  