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 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
|Edition description:||Softcover reprint of the original 1st ed. 1987|
|Product dimensions:||6.69(w) x 9.61(h) x 0.02(d)|
About the Author
Eli Maor is the author of Beautiful Geometry (with Eugen Jost), Venus in Transit, Trigonometric Delights, e: The Story of a Number, and The Pythagorean Theorem: A 4,000-Year History (all Princeton).
Table of ContentsI. 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 eThree 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 Möbius Strip.- 19. The Magic World of Mirrors.- 20. Horror Vacui, Amor Infiniti.- 21. Maurits C. EscherMaster 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.
Most Helpful Customer Reviews
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 addresses infinity in several categories: mathematical, geometry, art, and cosmology. The first two sections are basic background for the latter two. There is a whole chapter on M. C. Escher. This is an accessible and interesting treatment of the topic. Highly recommended for those interested in infinity and the historical, philosophical, and cultural connections.