The Irrationals

Julian Havil is the author of Gamma: Exploring Euler's Constant, Nonplussed!: Mathematical Proof of Implausible Ideas, Impossible?: Surprising Solutions to Counterintuitive Conundrums, and John Napier: Life, Logarithms, and Legacy (all Princeton). He is a retired former master at Winchester College, England, where he taught mathematics for more than three decades.

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 Apery 286 Appendix E Equivalence Relations 289 Appendix F The Mean Value Theorem 294 Index 295