Contents
Foreword ix
Acknowledgements xi
Introduction 1
§1. A sketch of our problem 1
§2. Some notation 3
Exercises 5
Chapter 1. The

n theory 7
§1. Erd˝ os’ original argument 7
§2. Higher dimensions 9
§3. Arbitrary metrics 11
Exercises 13
Chapter 2. The
n2/3 theory 15
§1. The Erd˝ os integer distance principle 15
§2. Moser’s construction 16
Exercises 20
Chapter 3. The Cauchy-Schwarz inequality 23
§1. Proof of the Cauchy-Schwarz inequality 23
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