The Irrationals:
A Story of the Numbers You Can't Count On
Julian Havil

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Introduction [in PDF format]

TABLE OF CONTENTS:

Acknowledgments ix

Introduction 1

Chapter One Greek Beginnings 9
Chapter Two The Route to Germany 52
Chapter Three Two New Irrationals 92
Chapter Four Irrationals, Old and New 109
Chapter Five A Very Special Irrational 137
Chapter Six From the Rational to the Transcendental 154
Chapter Seven Transcendentals 182
Chapter Eight Continued Fractions Revisited 211
Chapter Nine The Question and Problem of Randomness 225
Chapter Ten One Question, Three Answers 235
Chapter Eleven Does Irrationality Matter? 252

Appendix A The Spiral of Theodorus 272
Appendix B Rational Parameterizations of the Circle 278
Appendix C Two Properties of Continued Fractions 281
Appendix D Finding the Tomb of Roger Apéry 286
Appendix E Equivalence Relations 289
Appendix F The Mean Value Theorem 294

Index 295

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