3. Two New Irrationals

Chapters in this book

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