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

The Irrationals: A Story of the Numbers You Can't Count On
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The Irrationals: A Story of the Numbers You Can't Count On, The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular, The Irrationals: A Story of the Numbers You Can't Count On
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  • The Irrationals: A Story of the Numbers You Can't Count On
  • Written by author Julian Havil
  • Published by Princeton University Press, 7/22/2012
  • The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular
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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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The Irrationals: A Story of the Numbers You Can't Count On, The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In <i>The Irrationals</i>, the first popular, The Irrationals: A Story of the Numbers You Can't Count On

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The Irrationals: A Story of the Numbers You Can't Count On, The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In <i>The Irrationals</i>, the first popular, The Irrationals: A Story of the Numbers You Can't Count On

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

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The Irrationals: A Story of the Numbers You Can't Count On, The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In <i>The Irrationals</i>, the first popular, The Irrationals: A Story of the Numbers You Can't Count On

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

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