Leonhard Euler and the Bernoullis : mathematicians from Basel

"In the 17th century, the small but culturally and intellectually eminent city of Basel was the home of one of the most prominent mathematical families of all time, the Bernoullis, and their friend, protege, and master Leonhard Euler. The author chronicles their lives and achievements at a time when modern analysis and its applications to physics burst on the scene and created a methodological framework for modern science. Written for young adults, this book conveys the excitement of a scientific culture that impacts our life to this day and will serve as an inspiration to gifted young people to devote their lives to scientific pursuits."--[Résumé de l'éditeur] 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 1. The Bernoullis As Huguenots -- 2. The Bernoulli Family In Frankfurt And Then Basel -- 3. Jacob Makes His First Steps In The Study Of Mathematics -- 4. His Little Brother Johann 'helps' Jacob With Mathematics -- 5. Having Completed His Studies In Philosophy And Theology, Jacob Moves On -- 6. Jacob Travels To Geneva And Meets Elizabeth Waldkirch And Her Family -- 7. Jacob Teaches Elizabeth Waldkirch To Read And Write Numbers And Words -- 8. Sundials, And Tutoring In France -- 9. Jacob Meets With Mathematicians In Paris -- 10. Jacob Travels To Holland And England -- 11. Jacob Settles Into Life In Basel To Lecture And Learn -- 12. Leibniz's Calculus Vs. Newton's Fluxions -- 13. Johann Bernoulli Grows Up -- 14. Two Curves Studied By The Bernoullis : The Isochrone And The Catenary -- 15. More Mathematical Challenges From The Bernoullis -- 16. Jacob Bernoulli's Mathematics -- 17. Johann Bernoulli Returns To Basel With His Family -- 18. Johann Bernoulli's Son Daniel Grows Up --^ 19. Daniel Bernoulli, The Paris Prize, And The Longitude Problem -- 20. Leonhard Euler -- 21. Leonhard Euler's Early Education -- 22. Leonhard Euler Goes To The Latin School In Basel And Then On To The University -- 23. Daniel And Nicolaus Bernoulli Receive A Call To The Academy At St. Petersburg -- 24. The Academy Of Sciences At St. Petersburg -- 25. Euler Begins His Career And Moves To St. Petersburg -- 26. Daniel Bernoulli And Leonhard Euler : An Active Scientific Partnership -- 27. The St. Petersburg Paradox -- 28. Euler's Early Work In St. Petersburg -- 29. Daniel Returns To Basel, And Leonhard Euler Becomes Professor Of Mathematics At St. Petersburg -- 30. Daniel Bernhoulli : A Famous Scholar -- 31. Leonhard Euler : Admired Professor At St. Petersburg -- 32. Euler Becomes Blind In His Right Eye -- 33. St. Petersburg Loses Euler To Frederick The Great Of Prussia -- 34. The Eulers Arrive At The Court Of Frederick The Great In Berlin -- 35. Euler's Scientific Work In Berlin --^ 36. Euler's Work In Number Theory -- 37. Magic Squares -- 38. Catherine The Great Invites Euler To Return To St. Petersburg -- 39. The Basel Clan. M.b.w. Tent. Includes Index. The Bernoullis as Huguenots. The Bernoulli family in Frankfurt and then Basel. Jacob makes his first steps in the study of mathematics. His little brother Johann “helps” Jacob with mathematics. Having completed his studies in philosophy and theology, Jacob moves on. Jacob travels to Geneva and meets Elizabeth Waldkirch and her family. Jacob teaches Elizabeth Waldkirch to read and write numbers and words. Sundials, and tutoring in France. Jacob meets with mathematicians in Paris. Jacob travels to Holland and England. Jacob settles into life in Basel to lecture and learn. Leibniz’s calculus vs. Newton’s fluxions. Johann Bernoulli grows up. Two curves studied by the Bernoullis: the isochrone and the catenary. Two more mathematical challenges from the Bernoullis. Jacob Bernoulli’s mathematics. Johann Bernoulli returns to Basel with his family. Johann Bernoulli’s son Daniel grows up. Daniel Bernouli, the Paris prize, and the longitude problem. Leonhard Euler. Leonhard Euler’s early education. Leonhard Euler goes to the Latin School in Basel and then on to the University. Daniel and Nicolaus Bernoulli receive a call to the Academy at St. Petersburg. The Academy of Sciences at St. Petersburg. Euler begins his career and moves to St. Petersburg. Daniel Bernoulli and Leonhard Euler: an active scientific partnership. The St. Petersburg paradox. Euler’s early work in St. Petersburg. Daniel returns to Basel, and Leonhard Euler becomes professor of mathematics at St. Petersburg. Daniel Bernoulli: a famous scholar. Leonhard Euler: admired professor at St. Petersburg. Euler becomes blind in his right eye. St. Petersburg loses Euler to Frederick the Great of Prussia. The Eulers arrive at the Court of Frederick the Great in Berlin. Euler’s scientific work in Berlin. Euler’s work in number theory. Magic squares. Catherine the Great invites Euler to return to St. Petersburg. The Basel clan. Index. "In the 17th century, the small but culturally and intellectually eminent city of Basel was the home of one of the most prominent mathematical families of all time, the Bernoullis, and their friend, protege, and master Leonhard Euler. The author chronicles their lives and achievements at a time when modern analysis and its applications to physics burst on the scene and created a methodological framework for modern science. Written for young adults, this book conveys the excitement of a scientific culture that impacts our life to this day and will serve as an inspiration to gifted young people to devote their lives to scientific pursuits."--[Résumé de l'éditeur] 'Leonhard Euler and the Bernoullis is a fascinating tale of the Bernoulli family and Euler's association with them. Successful merchants in the 16th and 17th centuries, the Bernoullis were driven out of Antwerp during the persecution of the Huguenots and settled first in Frankfurt, and then in Basel, where one of the most remarkable mathematical dy