Contents

Acknowledgments

Introduction

CHAPTER ONE

Greek Beginnings

CHAPTER TWO

The Route to Germany

CHAPTER THREE

Two New Irrationals

CHAPTER FOUR

Irrationals, Old and New

CHAPTER FIVE

A Very Special Irrational

CHAPTER SIX

From the Rational to the Transcendental

CHAPTER SEVEN

Transcendentals

CHAPTER EIGHT

Continued Fractions Revisited

CHAPTER NINE

The Question and Problem of Randomness

CHAPTER TEN

One Question, Three Answers

CHAPTER ELEVEN

Does Irrationality Matter?

APPENDIX A

The Spiral of Theodorus

APPENDIX B

Rational Parameterizations of the Circle

APPENDIX C

Two Properties of Continued Fractions

APPENDIX D

Finding the Tomb of Roger Apéry

APPENDIX E

Equivalence Relations

APPENDIX F

The Mean Value Theorem

Index