{"product_id":"the-banach-tarski-paradox-grzegorz-tomkowicz-9781107617315","title":"The Banach-Tarski Paradox","description":"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Grzegorz Tomkowicz, Stan Wagon\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1107617316\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781107617315\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Cambridge University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/19\/2019\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 366\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.13lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.76d","brand":"Grzegorz Tomkowicz","offers":[{"title":"Paperback","offer_id":43986439373055,"sku":"9781107617315","price":57.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_1eeae72d-9216-4824-91de-79a58d86c2a4.jpg?v=1683283349","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-banach-tarski-paradox-grzegorz-tomkowicz-9781107617315","provider":"WR Book House","version":"1.0","type":"link"}