Table of Contents

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.

Promotional Information

A collection of lively expository columns on the work of Euler, written by a leading scholar.

About the Author

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.

Reviews

…There are several ways to read this book. First, one may choose simply to open it at random to read Sandifer's discussion of how Euler attacked and thought about certain problems. Sandifer places Euler's work into context of the mathematics of his time, then describes what Euler did and how he did it and why it mattered, keeping in mind the advice of John Fauvel that Sandifer references in How Euler Did It: "Content, Context and Significance." An alternative would be to read the columns for particular topics that Euler considered; the columns are organized into sections on geometry, number theory, combinatorics, analysis, applied mathematics, and Euleriana… A third way to read this book would seem to summarize a great deal of Sandifer's writing on Euler… If you haven't yet dipped into these books, I'd encourage you to do so." - Joel Haack, MAA Reviews

"…On the whole, this collection is notable for the clarity of its exhibition, the wide range of subjects, and the sophistication of its mathematical treatment. One comes away with a renewed appreciation for the genius of Euler, as well as an improved understanding of what mathematical practice in the eighteenth century really looked like. Anyone with an interest in Euler or the development of mathematics in the eighteenth century will find a wealth of important material here." - Douglas M. Jesseph, Mathematical Reviews Clippings

"…Like the other books in the series this one is also very readable and gives once more insights into the works of Leonhard Euler." - Zentrallblatt