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.

• PrefacePart I: Geometry1. The Euler Line (January 2009)2. A Forgotten Fermat Problem (December 2008)3. A Product of Secants (May 2008)4. Curves and Paradox (October 2008)5. Did Euler Prove Cramer's Rule (November 2009 - A Guest Column by Rob Bradley)Part II: Number Theory6. Factoring F5 (March 2007)7. Rational Trigonometry (March 2008)8. Sums (and Differences) that are Squares (March 2009)Part III: Combinatorics9. St. Petersburg Paradox (July 2007)10. Life and Death - Part 1 (July 2008)11. Life and Death - Part 2 (August 2008)Part IV: Analysis12. e, π, and i: Why is "Euler" in the Euler Identity (August 2007)13. Multi-zeta Functions (January 2008)14. Sums of Powers (June 2009)15. A Theorem of Newton (April 2008)16. Estimating π (February 2009)17. Nearly a Cosine Series (May 2009)18. A Series of Trigonometric Powers (June 2008)19. Gamma the Function (September 2007)20. Gamma the Constant (October 2007)21. Partial Fractions (June 2007)22. Inexplicable Functions (November 2007)23. A False Logarithm Series (December 2007)24. Introduction to Complex Variables (May 2007)25. The Moon and the Differential (October 2009 - A Guest Column by Rob Bradley)Part V: Applied Mathematics26. Density of Air (July 2009) 27. Bending Light (August 2009) 28. Saws and Modeling (November 2008)29. PDEs of Fluids (September 2008)30. Euler and Gravity (December 2009 - A Guest Column by Dominic Klyve)Part VI: Euleriana31. Euler and the Hollow Earth: Fact or Fiction? (April 2007) 32. Fallible Euler (February 2008)33. Euler and the Pirates (April 2009)34. Euler as a Teacher - Part 1 (January 2010)35. Euler as a Teacher - Part 2 (February 2010)About the Author

…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