Leonhard Euler and the Bernoullis: Mathematicians from Basel

Cover......Page 1
Title......Page 3
Copyright......Page 4
Contents......Page 6
Preface......Page 9
Acknowledgements......Page 12
Figure Credits......Page 16
1. The Bernoullis as Huguenots......Page 17
2. The Bernoulli Family in Frankfurt and Then Basel......Page 23
3. Jacob Makes His First Steps in the Study of Mathematics......Page 28
4. His Little Brother Johann \"Helps\" Jacobwith Mathematics......Page 35
5. Having Completed His Studies in Philosophy and Theology, Jacob Moves On......Page 41
6. Jacob Travels to Geneva and Meets Elizabeth Waldkirch and Her Family......Page 47
7. Jacob Teaches Elizabeth Waldkirch to Read and Write Numbers and Words......Page 53
8. Sundials, and Tutoring in France......Page 60
9. Jacob Meets with Mathematicians in Paris......Page 66
10. Jacob Travels to Holland and England......Page 74
11. Jacob Settles into Life in Basel to Lecture and Learn......Page 78
12. Leibniz\'s Calculus vs. Newton\'s Fluxions......Page 90
13. Johann Bernoulli Grows Up......Page 99
14. Two Curves Studied by the Bernoullis: The Isochrone and the Catenary......Page 108
15. More Mathematical Challenges from the Bernoullis......Page 113
16. Jacob Bernoulli\'s Mathematics......Page 119
17. Johann Bernoulli Returns to Basel with His Family......Page 126
18. Johann Bernoulli’s Son Daniel Grows Up......Page 132
19. Daniel Bernoulli, the Paris Prize, and the Longitude Problem......Page 137
20. Leonhard Euler......Page 140
21. Leonhard Euler\'s Early Education......Page 145
22. Leonhard Euler Goes to the Latin School in Basel and Then on to the University......Page 149
23. Daniel and Nicolaus Bernoulli Receive a Call to the Academy at St. Petersburg......Page 155
24. The Academy of Sciences at St. Petersburg......Page 162
25. Euler Begins His Career and Moves to St. Petersburg......Page 165
26. Daniel Bernoulli and Leonhard Euler: An Active Scientific Partnership......Page 173
27. The St. Petersburg Paradox......Page 181
28. Euler\'s Early Work in St. Petersburg......Page 185
29. Daniel Returns to Basel, and Leonhard Euler Becomes Professor of Mathematics at St. Petersburg......Page 194
30. Daniel Bernoulli: A Famous Scholar......Page 203
31. Leonhard Euler: Admired Professor at St. Petersburg......Page 208
32. Euler Becomes Blind in His Right Eye......Page 215
33. St. Petersburg Loses Euler to Frederick the Great of Prussia......Page 218
34. The Eulers Arrive at the Court of Frederick the Great in Berlin......Page 224
35. Euler\'s Scientific Work in Berlin......Page 236
36. Euler\'s Work in Number Theory......Page 243
37. Magic Squares......Page 249
38. Catherine the Great Invites Euler to Return to St. Petersburg......Page 253
39. The Basel Clan......Page 261