## 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 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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An excellent companion book to Rudy Rucker's "Infinity and The Mind", George Gamows "One, Two, Three...Infinity" and Jean Pierre Ady Fenyo's "The Most Important Thought". If you are truly interested in exploring the idea of Infinity then these are all great books worth your time.

### 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 | |