Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills (Princeton Science Library)

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9780691118222: Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills (Princeton Science Library)



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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From the Inside Flap:


"If you ever wondered about the beauties and powers of mathematics, this book is a treasure trove. Paul Nahin uses Euler's formula as the magic key to unlock a wealth of surprising consequences, ranging from number theory to electronics, presented clearly, carefully, and with verve."--Peter Pesic, St. John's College


"The range and variety of topics covered here is impressive. I found many little gems that I have never seen before in books of this type. Moreover, the writing is lively and enthusiastic and the book is highly readable."--Des Higham, University of Strathclyde, Glasgow


About the Author:

Paul J. Nahin is Professor Emeritus of Electrical Engineering at the University of New Hampshire. He is the author of Duelling Idiots and Other Probability Puzzlers, When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible, and An Imaginary Tale: The Story of!-1 (all Princeton). Nahin is Professor Emeritus of Electrical Engineering at the University of New Hampshire. He and his wife Pat live with three enormous tabby cats in a country cape in Lee, New Hampshire.

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Nahin, Paul J.
Editore: Princeton University Press
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