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The Banach–Tarski Paradox (Encyclopedia of Mathematics and its Applications, Series Number 163) - Hardcover
Synopsis
The Banach-Tarski Paradox is a most striking mathematical construction: it asserts that a solid ball can be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large. This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, set theory, and logic. This new edition of a classic book unifies contemporary research on the paradox. It has been updated with many new proofs and results, and discussions of the many problems that remain unsolved. Among the new results presented are several unusual paradoxes in the hyperbolic plane, one of which involves the shapes of Escher's famous 'Angel and Devils' woodcut. A new chapter is devoted to a complete proof of the remarkable result that the circle can be squared using set theory, a problem that had been open for over sixty years.
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Book Description
The Banach-Tarski Paradox is the most surprising result in mathematics. This new edition of a classic book offers a comprehensive, accessible presentation, with many related results, especially connections to non-Euclidean geometry, to squaring the circle, and even to some art by Escher. This material is suited to projects for undergraduates or masters students.
About the Author
Grzegorz Tomkowicz is a self-educated Polish mathematician who has made several important contributions to the theory of paradoxical decompositions and invariant measures.
Stan Wagon is a Professor of Mathematics at Macalester College, Minnesota. He is a winner of the Wolfram Research Innovator Award, as well as numerous writing awards including the Ford, Evans, and Allendoerfer Awards. His previous work includes A Course in Computational Number Theory (2000), The SIAM 100-Digit Challenge (2004), and Mathematica® in Action, 3rd edition (2010).
"About this title" may belong to another edition of this title.
- PublisherCambridge University Press
- Publication date2016
- ISBN 10 1107042593
- ISBN 13 9781107042599
- BindingHardcover
- LanguageEnglish
- Edition number2
- Number of pages360
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Hardcover. Condition: new. Hardcover. The Banach-Tarski Paradox is a most striking mathematical construction: it asserts that a solid ball can be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large. This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, set theory, and logic. This new edition of a classic book unifies contemporary research on the paradox. It has been updated with many new proofs and results, and discussions of the many problems that remain unsolved. Among the new results presented are several unusual paradoxes in the hyperbolic plane, one of which involves the shapes of Escher's famous 'Angel and Devils' woodcut. A new chapter is devoted to a complete proof of the remarkable result that the circle can be squared using set theory, a problem that had been open for over sixty years. The BanachTarski Paradox is the most surprising result in mathematics. This new edition of a classic book offers a comprehensive, accessible presentation, with many related results, especially connections to non-Euclidean geometry, to squaring the circle, and even to some art by Escher. This material is suited to projects for undergraduates or masters students. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781107042599
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