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How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?

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# How Euler Did It

How Euler Did It, vol III of The MAA Tercentenary Euler Celebration series, C. Edward Sandifer; 2007. 237 pp. hard cover, $51.95 ($41.95 member). ISBN:978-0-88385-563-8; Mathematical Association of America, Washington, D.C. 1-800-331-1622 or www.maa.org

This is the third volume of the MAA’s published tribute to Leonard Euler (1707-1783).  Its contents are a collection of forty “How Euler Did It” columns published by Ed Sandifer on MAA Online between November, 2003 and February, 2007.  They represent a potpourri of Euler accomplishments in a wide variety of mathematical topics and fields, ranging from geometry to number theory, to combinatorics, to applied areas such as astronomy, mechanics and even marine engineering. Certainly this selection of material attests to Euler’s varied interests and encompassing genius.  Illustrations and equations abound, drawing a reader actively into the mathematical situation being described.

Like people, books have personalities.  This is a pleasant book, one whose company I thoroughly enjoyed.  Edward Sandifer’s narration gently draws the reader along, supplying background information and explanations that enrich each presentation with a fuller appreciation of Euler’s times and work.  Each mathematical episode is short, six to eight pages, and is easily digestible.  Such an arrangement lends itself to leisurely reading.  Sandifer is an Euler scholar whose impressions help bring the mathematics alive.  While this book compliments the other two volumes of the series, it can certainly stand alone as an “Euler Reader,” a book that, in itself, provides an introduction to Leonard Euler’s life and work.  I highly recommend How Euler Did It for personal reading and library acquisition.

Frank Swetz, Professor Emeritus, The Pennsylvania State University