### Review

"Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful pure-mathematical 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 first-year undergraduate course in the UK."--

**Robin Wilson, ***London Mathematical Society Newsletter*

### 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**