How Euler Did ItHow Euler Did It is a collection of 40 monthly columns that appeared on MAA Online between November 2003 and February 2007 about the mathematical and scientific work of the great 18th century Swiss mathematician Leonhard Euler. Almost every column is self-contained and gives the context, significance and some of the details of a particular facet of his work. Professor Sandifer based his columns on Euler's own words in the original language in which they were written. In this way, the author was able to uncover many details that are not found in other sources. For example, we see how Euler used differential equations and continued fractions to prove that the constant e is irrational, several years before Lambert, who is usually credited with this discovery. Euler also made an observation equivalent to saying that the number of primes less than a number x is approximately x/Inx, an observation usually attributed to Gauss some 15 years after Euler died. The collection ends with a somewhat playful, but factual, account of Euler's role in the discovery on America. - Publisher. |
Contents
19th Century Triangle Geometry May 2006 | 19 |
Beyond Isosceles Triangles April 2004 | 29 |
Cramers Paradox August 2004 | 37 |
Fermats Little Theorem November 2003 | 45 |
Odd Perfect Numbers November 2006 | 57 |
Euler and Pell April 2005 | 63 |
2aa+bb January 2006 | 75 |
Philip Naudés Problem October 2005 | 85 |
Walliss Formula November 2004 | 153 |
Arc Length of an Ellipse October 2004 | 157 |
Mixed Partial Derivatives May 2004 | 163 |
Goldbachs Series February 2005 | 167 |
Bernoulli Numbers September 2005 | 171 |
Divergent Series June 2006 | 177 |
Who Proved e is Irrational? February 2006 | 185 |
Infinitely Many Primes March 2006 | 191 |
Venn Diagrams January 2004 | 91 |
Derangements September 2004 | 103 |
Orthogonal Matrices August 2006 | 109 |
Analysis | 113 |
Piecewise Functions January 2007 | 115 |
Finding Logarithms by Hand July 2005 | 121 |
Roots by Recursion June 2005 | 127 |
Theorema Arithmeticum March 2005 | 133 |
A Mystery about the Law of Cosines December 2004 | 139 |
A Memorable Example of False Induction August 2005 | 143 |
Foundations of Calculus September 2006 | 147 |
Formal Sums and Products July 2006 | 197 |
Estimating the Basel Problem December 2003 | 205 |
Basel Problem with Integrals March 2004 | 209 |
Cannonball Curves December 2006 | 213 |
Propulsion of Ships February 2004 | 219 |
How Euler Discovered America October 2006 | 223 |
The Euler Society May 2005 | 227 |
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About the Author 237 | |
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Common terms and phrases
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