Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills

Front Cover
Princeton University Press, 2006 - Mathematics - 380 pages
12 Reviews



I used to think math was no fun

'Cause I couldn't see how it was done

Now Euler's my hero

For I now see why zero

Equals e[pi] i+1



--Paul Nahin, electrical engineer



In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory.


This book is the sequel to Paul Nahin's An Imaginary Tale: The Story of I [the square root of -1], which chronicled the events leading up to the discovery of one of mathematics' most elusive numbers, the square root of minus one. Unlike the earlier book, which devoted a significant amount of space to the historical development of complex numbers, Dr. Euler begins with discussions of many sophisticated applications of complex numbers in pure and applied mathematics, and to electronic technology. The topics covered span a huge range, from a never-before-told tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for single-sideband AM radio, to the design of chase-and-escape problems.


The book is accessible to any reader with the equivalent of the first two years of college mathematics (calculus and differential equations), and it promises to inspire new applications for years to come. Or as Nahin writes in the book's preface: To mathematicians ten thousand years hence, "Euler's formula will still be beautiful and stunning and untarnished by time."


  

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Review: Dr Euler's Fabulous Formula: Cures Many Mathematical Ills

User Review  - Alex - Goodreads

Less playful and anecdotal than the title suggests, though the 'life of Euler' bit at the end and the historical references throughout the book fit that bill. But this is basically a solid math book ... Read full review

Review: Dr Euler's Fabulous Formula: Cures Many Mathematical Ills

User Review  - Alex Borghgraef - Goodreads

Less playful and anecdotal than the title suggests, though the 'life of Euler' bit at the end and the historical references throughout the book fit that bill. But this is basically a solid math book ... Read full review

Contents

IV
13
VI
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VII
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VIII
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IX
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X
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XI
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XXVIII
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XXIX
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XXX
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XXXI
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XXXIV
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XXXVIII
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XXXIX
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XL
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XLIV
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XLV
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Copyright

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Page 11 - This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.
Page xiv - I had a feeling once about Mathematics, that I saw it all Depth beyond depth was revealed to me the Byss and the Abyss. I saw, as one might see the transit of Venus or even the Lord Mayor's Show, a quantity passing through infinity and changing its sign from plus to minus. I saw exactly how it happened and why the tergiversation was inevitable: and how the one step involved all the others. It was like politics. But it was after dinner and I let it go!
Page 1 - Then, poets, discoverers, philosophers, and seers, in soft hats and long cloaks, looked their parts, and we newly-fledged freshmen gazed at them with admiration and awe. The appearance of Professor Benjamin Peirce, whose long gray hair, straggling grizzled beard and unusually bright eyes sparkling under a soft felt hat, as he walked briskly but rather ungracefully across the college yard, fitted very well with the opinion current among us that we were looking upon a real live genius, who had a touch...
Page 11 - During the three years which I spent at Cambridge my time was wasted, as far as the academical studies were concerned, as completely as at Edinburgh and at school.

About the author (2006)

Paul J. Nahin is professor emeritus of electrical engineering at the University of New Hampshire. He is the best-selling author of many popular-math books, including "Duelling Idiots and Other Probability Puzzlers," "The Logician and the Engineer," "Number-Crunching," "Mrs. Perkins's Electric Quilt," and "An Imaginary Tale" (all Princeton).

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