How Euler Did Even More

C. Edward Sandifer is Professor of Mathematics at Western Connecticut State University in Danbury, Connecticut. He is Secretary of The Euler Society (www.EulerSociety.org). His first book, The Early Mathematics of Leonhard Euler, was published by the MAA in December 2006, as part of the celebrations of Euler's tercentennial in 2007. The MAA published a collection of forty 'How Euler Did It' columns in June 2007.

Preface; Part I. Geometry: 1. The Euler line; 2. A forgotten Fermat problem; 3. A product of secants; 4. Curves and paradox; 5. Did Euler prove Cramer's Rule?; Part II. Number Theory: 6. Factoring F5; 7. Rational trigonometry; 8. Sums (and differences) that are squares; Part III. Combinatorics: 9. St Petersburg paradox; 10. Life and death – part 1; 11. Life and death – part 2; Part IV. Analysis: 12. e, π and i: why is 'Euler' in the Euler identity; 13. Multi-zeta functions; 14. Sums of powers; 15. A theorem of Newton; 16. Estimating π; 17. Nearly a cosine series; 18. A series of trigonometric powers; 19. Gamma the function; 20. Gamma the constant; 21. Partial fractions; 22. Inexplicable functions; 23. A false logarithm series; 24. Introduction to complex variables; 25. The Moon and the differential; Part V. Applied Mathematics: 26. Density of air; 27. Bending light; 28. Saws and modeling; 29. PDEs of fluids; 30. Euler and gravity; Part VI. Euleriana: 31. Euler and the hollow earth: fact or fiction?; 32. Fallible Euler; 33. Euler and the pirates; 34. Euler as a teacher – part 1; 35. Euler as a teacher – part 2; Index; About the author.