Book contents
- Frontmatter
- Dedication
- Epigraph
- Contents
- Foreword
- Addendum to the Foreword
- Preface
- Part One 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 Two Finitely Additive Measures, or the Nonexistence of Paradoxical Decompositions
- Appendices
- Bibliography
- List of Symbols
- Index
8 - Paradoxes in Low Dimensions
from Part One - Paradoxical Decompositions, or the Nonexistence of Finitely Additive Measures
Published online by Cambridge University Press: 05 June 2016
Book contents
- Frontmatter
- Dedication
- Epigraph
- Contents
- Foreword
- Addendum to the Foreword
- Preface
- Part One 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 Two Finitely Additive Measures, or the Nonexistence of Paradoxical Decompositions
- Appendices
- Bibliography
- List of Symbols
- Index
- Type
- Chapter
- Information
- The Banach–Tarski Paradox , pp. 116 - 132Publisher: Cambridge University PressPrint publication year: 2016