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."
Not one of the best books of Professor Nahin Well this time I don't agree with reviewers above in the sense that if we liked An Imaginary Tale, then this book would like us too.
Certainly I enjoyed a great deal An Imaginary Tale, but I hoped I would find much more in Dr Euler's Formula, as I was really very impressed the first time I met -in my second year of electrical engineering- the most beautiful equation in mathematics, as professor Nahin has pointed out, but I really was very dissapointed, that in this new book I did not find anything about the fact that Dr. Euler's Fabulous Formula is most remarkable because even with differentiation and integration the mathematical operations that represent change, Euler's Identity remains with the same form, except for being affected by the square root of minus one, i.e., by a process of rotation.
It is this remarkable property the one that permits
"to reduce steady-state sinusoidal problems to forms which are identical to those for resistive networks."
and that made that Charles Steinmetz was called
"the wizard who generated electricity from the square root of minus one"
when the great historical struggle between AC and DC current was solved by that famous paper of Steinmetz.
Yes, it was this remarkable property that made me think that Dr. Euler's Formula could cure not only many mathematical ills, but physical ones such as those of deducing both the pendulum formula and the Complex Schrodinger's wave equation, based in a complex metrics in which Euler's identity plays the fundamental role, an exercise that I did many years ago and put somewhere at LANL.
Of course, I highly recommend this book by professor Nahin, as you will find in it a real complement to Fourier series and Integrals and to the study of Dirac's impulse function in chapters 4 and 5 and an important application to electronics in chapter 6.
Great stuff, but what's the point? I came to this book because I enjoyed The Story of the Square Root of Minus One, another book by Paul Nahin. This book is of a very different nature: unlike that other book, this one is light on concepts and heavy on calculations.
I enjoyed it quite a bit, however, hence the 4 stars, because I like complicated-looking integrals, but let me be frank I could not help thinking throughout: what's the point? (and do I deserve to be treated to so many typos?)
What's the point? It shows many uses of Euler's formula, but without explaining why we should care. A couple of chapters are devoted to Fourier series and transforms: again, what's the point? Towards the end, Nahin writes something to the effect that he has "avoided giving physical interpretations to the mathematical calculations" and that's precisely the problem: until the end of the book where there are clear references to things like electricity and other waves, we are never told (or reminded) why these clever manipulations are important.
It was shocking not to see any reference to the Riemann hypothesis and zeta function, which are perhaps the most beautiful example of the use of Euler's formula.
To Nahin's credit, he goes through the calculations step by step, so that if you do care (for some reason) then you can follow pretty much the whole thing without breaking a sweat (Nahin did the hard work). But I will confess that I did skip a few pages here and there: my eyes and brains got tired and the nagging thought came, well, what's the point?
Thoroughly recommended, however.
Warning Don't buy this book without buying the companion i book by Paul Nahin. This is clearly meant as a supplement to the i book. Does not stand alone except maybe in the applications of the formula.
I gave this book 5 stars because I had no basis for judgment. The author clearly states in the beginning of the book that this book has many interesting things he couldn't fit in the first one.
Dr Euler's Fabulous Formula A very interesting book. I am a retired Electrical Engineer and hence find this book particularly interesting. Not for the faint hearted as it contains a very large amount of complex mathematics. Overall, very good.
Catchy title and cover graphic but reads like a textbook After the first few pages I got the feeling that this book was based on notes from a class that Nahin had taught. And sure enough, the acknowledgement section confirmed my suspicion (p. 375). Now, on its face, this isn't necessarily good or necessarily bad. But it can give you a hint of what the book might be like: the course notes were from two, third-year electrical engineering classes on systems engineering. And that's what the book reads like.
It's not what I expected with a title like Dr. Euler's Fabulous Formula. I doubt that's what Nahin's classes were called. The title is probably the doing of the publisher's marketing department, not Nahin. In addition, I think the title is actually misleading. I didn't do a page count but it seems like more pages are devoted to Fourier analysis, as opposed to anything else.
I have only a layperson's interest in math books, perhaps caused by having the worse calculus teacher in the universe. Even so, I should have looked for detailed reviews, rather than being seduced by the title. If I had, I might have known what to expect. But I didn't. I bought the book from Amazon but on the basis of an ad in Science News, I think it was. So I now have a very clean, once-read copy of this book for sale!
On a topic I don't believe is covered by other reviewers is Nahin's rant about Jackson Pollock's drip paintings as he attempts to discuss the beauty of theories and equations (p. xix of the Preface). That's why I bought the book in the first place: I was pursuing my interest in the clear and intriguing beauty of Euler's Fabulous Formula. However, I nearly stopped reading only a few pages in after Nahin's incredibly clichéd statement: ..."but anybody who can observe the result of throwing paint on canvas--what two-year olds routinely do in ten thousand day-care centers every day (my gosh, what I do every time I pain my ceiling)--and call the outcome art, much less beautiful art, is delusional or a least deeply confused (in my humble opinion)". Nahin says he places Norman Rockwell far above Pollock as an artist.
He doesn't leave it at that. In a footnote (p. 348), when discussing Pollock's use of a can with a hole in the bottom, he says: "a gravity-driven mechanical system did all of the `creative' work". That's somewhat like me saying that a friction device (Nahin's pencil?) was responsible for whatever "creative" work might be discovered in his book. (As an aside, the footnotes are enjoyable. I liked them as much as the text itself.)
Perhaps Nahin thought it was OK to put this screed in the Preface because it was, as he says, just his "opinion". The fact is, both Pollock and Rockwell are fabulous in their own right and this kind of reasoning made me distrust ANY judgment Nahin might make about beauty, mathematical or otherwise. Having done a little of both professional level science and art, and even a smattering of math (if you can count probability and statistics), I would agree with Nahin's wife, he is indeed a "cultural Neanderthal" (Preface, p. xix). Perhaps even a mathematical one. And to that list I would add, the stereotype of a grumpy, old fashioned.... On second though, I'm not going to say it. I have acquaintances that fortunately do not fit that stereotype.
Least I seem totally negative, Nahin does explain why Euler deserves an enormous amount or respect and admiration and I liked his explanation of Heisenberg's Uncertainty Principle (p. 255) and why Pi shows up in such strange places (p. 359-60).
So I give Nahin a 3 and his publisher a 1 (for misleading marketing). I think that's an arithmetic mean of 2, if my friction device serves me correctly.
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