The Banach-Tarski paradox:
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...
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| Previous Title: | Wagon, Stan The Banach-Tarski paradox |
|---|---|
| Main Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
New York
Cambridge University Press
[2016]
|
| Edition: | Second edition |
| Series: | Encyclopedia of mathematics and its applications
163 |
| Subjects: | |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 06 Jun 2016) |
| ISBN: | 9781107042599 9781107617315 |
Staff View
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| 520 | |a 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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| author | Tomkowicz, Grzegorz Wagon, Stan 1951- |
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| author_facet | Tomkowicz, Grzegorz Wagon, Stan 1951- |
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| dewey-full | 511.3/22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/22 |
| dewey-search | 511.3/22 |
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| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| language | English |
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| spelling | Tomkowicz, Grzegorz (DE-588)1119926203 aut The Banach-Tarski paradox Grzegorz Tomkowicz, Centrum Edukacji G2, Bytom, Poland; Stan Wagon, Macalester College, St. Paul, Minnesota Second edition New York Cambridge University Press [2016] © 2016 txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 163 Title from publisher's bibliographic system (viewed on 06 Jun 2016) 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 Banach-Tarski paradox Measure theory Decomposition (Mathematics) Zerlegung Mathematik (DE-588)4190746-2 gnd rswk-swf Banach-Tarskisches Paradoxon (DE-588)4143975-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Banach-Tarskisches Paradoxon (DE-588)4143975-2 s Maßtheorie (DE-588)4074626-4 s Zerlegung Mathematik (DE-588)4190746-2 s 1\p DE-604 Wagon, Stan 1951- (DE-588)172440114 aut Erscheint auch als Online-Ausgabe 978-1-107-61731-5 Vorangegangen ist Wagon, Stan The Banach-Tarski paradox 1985 Encyclopedia of mathematics and its applications 163 (DE-604)BV000903719 163 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Tomkowicz, Grzegorz Wagon, Stan 1951- The Banach-Tarski paradox Encyclopedia of mathematics and its applications Banach-Tarski paradox Measure theory Decomposition (Mathematics) Zerlegung Mathematik (DE-588)4190746-2 gnd Banach-Tarskisches Paradoxon (DE-588)4143975-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4190746-2 (DE-588)4143975-2 (DE-588)4074626-4 |
| title | The Banach-Tarski paradox |
| title_auth | The Banach-Tarski paradox |
| title_exact_search | The Banach-Tarski paradox |
| title_full | The Banach-Tarski paradox Grzegorz Tomkowicz, Centrum Edukacji G2, Bytom, Poland; Stan Wagon, Macalester College, St. Paul, Minnesota |
| title_fullStr | The Banach-Tarski paradox Grzegorz Tomkowicz, Centrum Edukacji G2, Bytom, Poland; Stan Wagon, Macalester College, St. Paul, Minnesota |
| title_full_unstemmed | The Banach-Tarski paradox Grzegorz Tomkowicz, Centrum Edukacji G2, Bytom, Poland; Stan Wagon, Macalester College, St. Paul, Minnesota |
| title_old | Wagon, Stan The Banach-Tarski paradox |
| title_short | The Banach-Tarski paradox |
| title_sort | the banach tarski paradox |
| topic | Banach-Tarski paradox Measure theory Decomposition (Mathematics) Zerlegung Mathematik (DE-588)4190746-2 gnd Banach-Tarskisches Paradoxon (DE-588)4143975-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Banach-Tarski paradox Measure theory Decomposition (Mathematics) Zerlegung Mathematik Banach-Tarskisches Paradoxon Maßtheorie |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT tomkowiczgrzegorz thebanachtarskiparadox AT wagonstan thebanachtarskiparadox |