OpenCourser
Learn skills that shape your future
Visit OpenCourser.com
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.
Save
Protected by Amazon A-to-z Guarantee & generous return policies
Every book purchase is protected by the Amazon A-to-z Guarantee. This guarantee covers both the condition of your book and its timely delivery, providing full buyer protection whether you purchase directly from Amazon or from third-party marketplace sellers.
Generous 30-day return policy on physical books. Amazon makes returns effortless with self-service return labels, drop-off at thousands of local locations (Kohl's, Whole Foods, UPS Stores), and free return shipping on eligible book purchases.
Maximize your savings with competitive pricing, deep discounts on new and used marketplace copies, bundled textbook rentals, and exclusive member savings through Amazon Prime with free fast delivery.
Read your way across versatile digital and physical formats: instant delivery via Kindle eBooks, unlimited reading with a Kindle Unlimited subscription, audiobook listening with Audible (often featuring a 30-day free trial), or traditional paperback and hardcover editions.
OpenCourser helps millions of learners each year. People visit us to learn workspace skills, ace their exams, and nurture their curiosity.
Our extensive catalog contains over 50,000 courses and twice as many books. Browse by search, by topic, or even by career interests. We'll match you to the right resources quickly.
Find this site helpful? Tell a friend about us.
We're supported by our community of learners. When you purchase or subscribe to courses and programs or purchase books, we may earn a commission from our partners.
Your purchases help us maintain our catalog and keep our servers humming without ads.
Thank you for supporting OpenCourser.
