Introduction

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Acknowledgments ix
4. Introduction 1
5. Chapter one. Greek Beginnings 9
6. Chapter Two. The Route to Germany 52
7. Chapter Three. Two New Irrationals 92
8. Chapter Four. Irrationals, Old and New 109
9. Chapter Five. A Very Special Irrational 137
10. Chapter Six. From the Rational to the Transcendental 154
11. Chapter Seven. Transcendentals 182
12. Chapter Eight. Continued Fractions Revisited 211
13. Chapter Nine. The Question and Problem of Randomness 225
14. Chapter Ten. One Question, Three Answers 235
15. Chapter Eleven. Does Irrationality Matter? 252
16. Appendix A. The Spiral of Theodorus 272
17. Appendix B. Rational Parameterizations of the Circle 278
18. Appendix C. Two Properties of Continued Fractions 281
19. Appendix D. Finding the Tomb of Roger Apéry 286
20. Appendix E. Equivalence Relations 289
21. Appendix F. The Mean Value Theorem 294
22. Index 295