To Infinity and Beyond : A Cultural History of the Infinite

By (author) Maor, Eli

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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[目次]

  • I. Mathematical Infinity.- 1. First Steps to Infinity.- Zero, One, Infinity.- 2. Towards Legitimation.- Numbers Large and Small.- 3. Convergence and Limit.- The Prime Numbers.- 4. The Fascination of Infinite Series.- 5. The Geometric Series.- 6. More about Infinite Series.- 7. Interlude: An Excursion into the Number Concept.- 8. The Discovery of Irrational Numbers.- ?, ?, and e-Three Celebrated Irrationals.- 9. Cantor's New Look at the Infinite.- 10. Beyond Infinity.- II. Geometric Infinity.- 11. Some Functions and Their Graphs.- Some Geometric Paradoxes Involving Infinity.- 12. Inversion in a Circle.- 13. Geographic Maps and Infinity.- 14. Tiling the Plane.- 15. A New Look at Geometry.- 16. The Vain Search for Absolute Truth.- III. Aesthetic Infinity.- 17. Rejoice the Infinite!.- 18. The Mobius Strip.- 19. The Magic World of Mirrors.- 20. Horror Vacui, Amor Infiniti.- 21. Maurits C. Escher-Master of the Infinite.- 22. The Modern Kabbalists.- IV. Cosmological Infinity.- 23. The Ancient World.- 24. The New Cosmology.- 25. The Horizons Are Receding.- 26. A Paradox and Its Aftermath.- 27. The Expanding Universe.- 28. The Modern Atomists.- 29. Which Way from Here?.- Epilogue.

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この本の情報

書名 To Infinity and Beyond : A Cultural History of the Infinite
著作者等 Maor, Eli
書名別名 A Cultural History of the Infinite
出版元 Springer-Verlag New York Inc.
刊行年月 2011.10.14
ページ数 300p
大きさ H244 x W170
ISBN 9781461253969
言語 英語
出版国 アメリカ合衆国
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