Grzegorz Tomkowicz, Stan Wagon (Minnesota Macalester College)

The Banach-Tarski Paradox

• Broschiertes Buch

Produktbeschreibung

The Banachâ 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.

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Produktdetails

• Encyclopedia of Mathematics and its Applications
• Verlag: Cambridge University Press
• 2 Revised edition
• Seitenzahl: 368
• Erscheinungstermin: 24. Mai 2019
• Englisch
• Abmessung: 234mm x 156mm x 20mm
• Gewicht: 636g
• ISBN-13: 9781107617315
• ISBN-10: 1107617316
• Artikelnr.: 57672103

Autorenporträt

Grzegorz Tomkowicz is a self-educated Polish mathematician who has made several important contributions to the theory of paradoxical decompositions and invariant measures.

Inhaltsangabe

Part I. Paradoxical Decompositions, or the Nonexistence of Finitely Additive Measures: 1. Introduction
2. The Hausdorff paradox
3. The Banach-Tarski paradox: duplicating spheres and balls
4. Hyperbolic paradoxes
5. Locally commutative actions: minimizing the number of pieces in a paradoxical decomposition
6. Higher dimensions
7. Free groups of large rank: getting a continuum of spheres from one
8. Paradoxes in low dimensions
9. Squaring the circle
10. The semigroup of equidecomposability types
Part II: Finitely Additive Measures, or the Nonexistence of Paradoxical Decompositions: 11. Transition
12. Measures in groups
13. Applications of amenability
14. Growth conditions in groups and supramenability
15. The role of the axiom of choice.