RT Book, Whole DB /z-wcorg/ DS http://worldcat.org ID 166427115 LA English T1 How Euler did it A1 Sandifer, Charles Edward,, PB Mathematical Association of America PP [Washington, DC] YR 2007 SN 9780883855638 0883855631 AB How 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.