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More About This Textbook
Overview
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 mideighteenth century, Swissborn 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 neverbeforetold tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for singlesideband AM radio, to the design of chaseandescape 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."
Editorial Reviews
From Barnes & Noble
"Lisez Euler, lisez Euler, c'est notre maître à tous." (Read Euler, read Euler, he is the master of us all.) PierreSimon Laplace's tribute to Swissborn mathematician Leonhard Euler (170783) might stand as the gateway to this standalone sequel to An Imaginary Tale. With memorable anecdotes, author Paul Nahin introduces readers to numerous advanced applications of complex numbers in pure and applied mathematics and to electronic technology. His writing skills and obvious enthusiasm for his topics convey the deep aesthetics and clarity of mathematical discoveries.Nature
Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful puremathematical identities. Most of his topics lie just beyond the periphery of a typical mathematics course: they are facts, such as the irrationality of pi, that you may have heard of but never had explained in detail. It would be good to have more books like this.New Scientist  Matthew Killeya
Nahin's tale of the formula e^{[pi]} i+1=0, which links five of the most important numbers in mathematics, is remarkable. With a plethora of historical and anecdotal material and a knack for linking events and facts, he gives the reader a strong sense of what drove mathematicians like Euler.MAA Reviews  Henry Ricardo
The author conducts a fascinating tour through pure and applied mathematics, physics, and engineering, from the ethereal heights of number theory to the earthiness of constructing speech scramblers. . . . [T]his is a marvelous book that will illuminate the mathematical landscape of complex numbers and their many applications.SIAM Review  Robert E. O'Malley
The heart and soul of the book are the final three chapters on Fourier series, Fourier integrals, and related engineering. One can recommend them to all applied math students for their historical development and sensible content.Mathematical Reviews  Eberhard Knobloch
This is a book for mathematicians who enjoy historically motivated mathematical explanations on a high mathematical level.London Mathematical Society Newsletter  Robin Wilson
It is a 'popular' book, written for a general reader with some mathematical background equivalent to a firstyear undergraduate course in the UK."Nature othy Gowers
Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful puremathematical identities. Most of his topics lie just beyond the periphery of a typical mathematics course: they are facts, such as the irrationality of pi, that you may have heard of but never had explained in detail. It would be good to have more books like this.
From the Publisher
"Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful puremathematical identities. Most of his topics lie just beyond the periphery of a typical mathematics course: they are facts, such as the irrationality of pi, that you may have heard of but never had explained in detail. It would be good to have more books like this."—Timothy Gowers,Nature"Nahin's tale of the formula e^{[pi]} i+1=0, which links five of the most important numbers in mathematics, is remarkable. With a plethora of historical and anecdotal material and a knack for linking events and facts, he gives the reader a strong sense of what drove mathematicians like Euler."—Matthew Killeya, New Scientist
"What a treasure of a book this is! This is the fourth enthusiastic, informative, and delightful book Paul Nahin has written about the beauties of various areas of mathematics. . . . This book is a marvelous tribute to Euler's genius and those who built upon it and would make a great present for students of mathematics, physics, and engineering and their professors. Paul Nahin's name has been added to my list of those with whom I wouldn't mind being stranded on a desert island—not only would he be informative and entertaining, but he would probably be able to rig a signaling device from sea water and materials strewn along the beach."—Henry Ricardo, MAA Reviews
"The heart and soul of the book are the final three chapters on Fourier series, Fourier integrals, and related engineering. One can recommend them to all applied math students for their historical development and sensible content."—Robert E. O'Malley, Jr., SIAM Review
"It is very difficult to sum up the greatness of Euler. . . . This excellent book goes a long way to explaining the kind of mathematician he really was."—Mathematics Today
"The author conducts a fascinating tour through pure and applied mathematics, physics, and engineering, from the ethereal heights of number theory to the earthiness of constructing speech scramblers. . . . [T]his is a marvelous book that will illuminate the mathematical landscape of complex numbers and their many applications."—Henry Ricardo, Mathematics Teacher
"This is a book for mathematicians who enjoy historically motivated mathematical explanations on a high mathematical level."—Eberhard Knobloch, Mathematical Reviews
"It is a 'popular' book, written for a general reader with some mathematical background equivalent to a firstyear undergraduate course in the UK."—Robin Wilson, London Mathematical Society Newsletter
New Scientist
Nahin's tale of the formula e^{[pi]} i+1=0, which links five of the most important numbers in mathematics, is remarkable. With a plethora of historical and anecdotal material and a knack for linking events and facts, he gives the reader a strong sense of what drove mathematicians like Euler.— Matthew Killeya
MAA Reviews
What a treasure of a book this is! This is the fourth enthusiastic, informative, and delightful book Paul Nahin has written about the beauties of various areas of mathematics. . . . This book is a marvelous tribute to Euler's genius and those who built upon it and would make a great present for students of mathematics, physics, and engineering and their professors. Paul Nahin's name has been added to my list of those with whom I wouldn't mind being stranded on a desert island—not only would he be informative and entertaining, but he would probably be able to rig a signaling device from sea water and materials strewn along the beach.— Henry Ricardo
SIAM Review
The heart and soul of the book are the final three chapters on Fourier series, Fourier integrals, and related engineering. One can recommend them to all applied math students for their historical development and sensible content.— Robert E. O'Malley, Jr.
Mathematics Today
It is very difficult to sum up the greatness of Euler. . . . This excellent book goes a long way to explaining the kind of mathematician he really was.Mathematics Teacher
The author conducts a fascinating tour through pure and applied mathematics, physics, and engineering, from the ethereal heights of number theory to the earthiness of constructing speech scramblers. . . . [T]his is a marvelous book that will illuminate the mathematical landscape of complex numbers and their many applications.— Henry Ricardo
Mathematical Reviews
This is a book for mathematicians who enjoy historically motivated mathematical explanations on a high mathematical level.— Eberhard Knobloch
London Mathematical Society Newsletter
It is a 'popular' book, written for a general reader with some mathematical background equivalent to a firstyear undergraduate course in the UK.— Robin Wilson
New Scientist
Nahin's tale of the formula e[pi] i+1=0, which links five of the most important numbers in mathematics, is remarkable. With a plethora of historical and anecdotal material and a knack for linking events and facts, he gives the reader a strong sense of what drove mathematicians like Euler.— Matthew Killeya
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Meet 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 I [the square root of 1]" (all Princeton).
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