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Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills
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. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.
416 pages, Paperback
First published April 10, 2006
94 people are currently reading
1187 people want to read
About the author
Paul J. Nahin
53 books125 followersPaul J. Nahin is professor emeritus of electrical engineering at the University of New Hampshire and the author of many best-selling popular math books, including The Logician and the Engineer and Will You Be Alive 10 Years from Now? (both Princeton).
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Displaying 1 - 20 of 20 reviews
March 21, 2021
Better than Prozac
Euler’s formula is arguably the most beautiful construction in mathematics. It shows how, with unparalleled elegance, five incommensurables universes of numbers are related to one another. Nahin makes the argument wonderfully and shows how the identity’s simple beauty is just as much use as ornament, solving a variety of mathematical problems in novel ways. Although not directed toward mathematicians, the book does require some competence in trigonometry, calculus, and elementary numerical analysis, probably obtained through study in engineering or physics. If you can handle it, I think you’ll find it comforting just how consistent, coherent and stable mathematics can be in a rapidly changing world.
Euler’s formula is arguably the most beautiful construction in mathematics. It shows how, with unparalleled elegance, five incommensurables universes of numbers are related to one another. Nahin makes the argument wonderfully and shows how the identity’s simple beauty is just as much use as ornament, solving a variety of mathematical problems in novel ways. Although not directed toward mathematicians, the book does require some competence in trigonometry, calculus, and elementary numerical analysis, probably obtained through study in engineering or physics. If you can handle it, I think you’ll find it comforting just how consistent, coherent and stable mathematics can be in a rapidly changing world.
December 2, 2020
Actually, this book is over my head. Tons of very well laid-out math on complex topics. To read this book you should have a mathematical background equivalent to what a beginning third year college undergraduate in an engineering or physics program of study would have completed. So, done with Calculus, Differential Equations, Linear Algebra, Probability/Statistics. And you need to LIKE your Math!
The math on page 22 has the Cayley-Hamilton theorem, alpha and beta characters both super and sub-scripted, matrices of sin and cos terms, the Identity matrix, and De Moivre's Theorem. On this same page are phrases like: "not hard to establish", "simply take it as plausible", "refer to any good book on linear algebra", "all we have left to do", "a straightforward task", "equations are easy to solve for", "I'll let you do the algebra to confirm", "actually easily handled", "actually don't have to worry about that particular problem"
While I like math, and I'm an EE/Physics person, I am out-of-shape for this intensity level of math. I fully read ch 1, and then skimmed the rest of the book. The final 22 pages on Euler paint a nice bio. The author describes this book as a "second half" to his 1998 publication: An Imaginary Tale: The Story of the Square Root of Minus One Maybe I'll go and try to read that book first.
1)Complex Numbers (matrices, 2D vectors, complex indeed!)
2)Vector Trips
3)Irrationality of pi^2
4)Fourier Series
5)Fourier Integrals
6)Electronics and sqrt(-1)
Euler: The Man and the Mathematical Physicist
The math on page 22 has the Cayley-Hamilton theorem, alpha and beta characters both super and sub-scripted, matrices of sin and cos terms, the Identity matrix, and De Moivre's Theorem. On this same page are phrases like: "not hard to establish", "simply take it as plausible", "refer to any good book on linear algebra", "all we have left to do", "a straightforward task", "equations are easy to solve for", "I'll let you do the algebra to confirm", "actually easily handled", "actually don't have to worry about that particular problem"
While I like math, and I'm an EE/Physics person, I am out-of-shape for this intensity level of math. I fully read ch 1, and then skimmed the rest of the book. The final 22 pages on Euler paint a nice bio. The author describes this book as a "second half" to his 1998 publication: An Imaginary Tale: The Story of the Square Root of Minus One Maybe I'll go and try to read that book first.
1)Complex Numbers (matrices, 2D vectors, complex indeed!)
2)Vector Trips
3)Irrationality of pi^2
4)Fourier Series
5)Fourier Integrals
6)Electronics and sqrt(-1)
Euler: The Man and the Mathematical Physicist
March 20, 2017
Having just finished this, may be I am too overwhelmed and brain-fucked to immediately judge the book, still I've got to say, this read was a treat to my soul.
This was a great homage to the ever so legendary Euler. The author did a tremendous job doing extensive research and putting together magnificent jewels from various fields of mathematics, physics and engineering, and all revolving around the one Fabulous Formula. I cannot imagine a book on applied mathematics getting any better than this.
If you have the mindset and of course enough time to work out some integrals (just kidding, you will have to do a lot more than that) and a certain weakness for beauty (100% platonic, mind you!), I would highly recommend this to you. Hope this book finds you in those awesome awestruck moments, when your mind goes "How the fuckkk!!!", just as it found me. Cheers!
This was a great homage to the ever so legendary Euler. The author did a tremendous job doing extensive research and putting together magnificent jewels from various fields of mathematics, physics and engineering, and all revolving around the one Fabulous Formula. I cannot imagine a book on applied mathematics getting any better than this.
If you have the mindset and of course enough time to work out some integrals (just kidding, you will have to do a lot more than that) and a certain weakness for beauty (100% platonic, mind you!), I would highly recommend this to you. Hope this book finds you in those awesome awestruck moments, when your mind goes "How the fuckkk!!!", just as it found me. Cheers!
August 5, 2014
Fantastic book. In no way is this a book for the layman, but so long as you have finished calculus, know a fair amount of linear algebra, and are willing to work as you read and actually absorb the material, you can get an amazing amount of understanding from the book. It deals largely with the applications of Euler's Identity, so most people in math sciences will be able to gain some amount of understanding from it. However, there aren't many pure mathematical sections in it, minus the first and third chapters. It's a great book, but certainly not for the layperson. I'd recommend it to anyone with a strong background in mathematics.
July 26, 2022
The book is a love letter to Euler and his mathematics, from a mathematician and electrical engineer. I applaud the sentiment. The “Fabulous Formula” is indeed a wonderful thing, one of many amazing creations (or are they discoveries?) from Euler’s prolific mind. I agree with Nahin that this is one of the most beautful things ever expressed by humans, a formula relating the transcendental (in every way) numbers e and pi, the most fundamental constants 0 and 1, and the enigmatic “imaginary” number i, along with the basic mathematical operations of multiplication and addition, via sines and cosines that capture periodicity…and it does it all in just SEVEN CHARACTERS (e to the i times pi plus one equals 0).
Rahin takes us on an excursion through Fourier analysis, irrational and transcendental numbers, and even some electrical engineering. The first chapter, on the “imaginary” number square root of negative one, is well worth reading. I wonder if his book length treatment of that number is as good as this single chapter.
But I did not enjoy this book, nor did I find it very enlightening. I wanted to. I have some serious mathematical training, and have published mathematics research in prestigious journals. But I was lost so thoroughly and so often by the presentation here that I ended up just skimming entire chunks.
The problem is: who is the target audience for this book? Nahin claims in the preface that it should be accessible to any person with an undergraduate degree in mathematics. I doubt it. This requires real and complex analysis, advanced calculus, and even some electronic engineering. There are page after page of integrals, a mind numbing parade. I get the impression that most of the book is written for an audience of one: the author.
And that’s a pity. It would be a wonderful thing to let people know more about Euler and the beautiful mathematics with his name attached. Unfortunately, each chapter here piles a new opaque formula on top of opaque formula, in an attempt to show the power of Euler’s formula. Instead, with each chapter, the original formula gets buried deeper and deeper in a pile of arcane notation (and the annoying recurrent admonition to “notice carefully”).
Rahin takes us on an excursion through Fourier analysis, irrational and transcendental numbers, and even some electrical engineering. The first chapter, on the “imaginary” number square root of negative one, is well worth reading. I wonder if his book length treatment of that number is as good as this single chapter.
But I did not enjoy this book, nor did I find it very enlightening. I wanted to. I have some serious mathematical training, and have published mathematics research in prestigious journals. But I was lost so thoroughly and so often by the presentation here that I ended up just skimming entire chunks.
The problem is: who is the target audience for this book? Nahin claims in the preface that it should be accessible to any person with an undergraduate degree in mathematics. I doubt it. This requires real and complex analysis, advanced calculus, and even some electronic engineering. There are page after page of integrals, a mind numbing parade. I get the impression that most of the book is written for an audience of one: the author.
And that’s a pity. It would be a wonderful thing to let people know more about Euler and the beautiful mathematics with his name attached. Unfortunately, each chapter here piles a new opaque formula on top of opaque formula, in an attempt to show the power of Euler’s formula. Instead, with each chapter, the original formula gets buried deeper and deeper in a pile of arcane notation (and the annoying recurrent admonition to “notice carefully”).
September 30, 2011
I have to admit: I didn't read the chapter on electronics and could not understand most of the Fourier integrals...
March 3, 2016
Many interesting ideas pertaining fourier theory and also the use of complex exponential forms. Will touch this again once advanced maths is mastered.
January 26, 2010
I picked this one up thinking it would be a math history book (and because it had a great cover!), but it turned out to be more of a math book. Which would have been fine if I had ever taken advanced number theory or electrical engineering courses, but I hadn't. Still, I broke out my calculus textbook and followed along as best I could. Probably absorbed 60% of it. When writing prose instead of formulas, the author is witty and engaging. I'd like to read a pure history of math book by him.
September 30, 2014
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 on complex numbers, Fourier analysis and a bit of electronics, which may deter many readers expecting math history.
May 12, 2012
Ya need to know a little math, but super awesome. Euler must of been an incredible intellect!
July 20, 2022
Dr. Euler's Fabulous Formula is a sequel to An Imaginary Tale, a book on imaginary numbers by Paul J Nahin. The eponymous formula links the exponential function, the ratio of a circle's diameter to its circumference, imaginary numbers, one, and zero. Euler's Equation is simple and beautiful.
As you all know, Leonhard Euler was a genius mathematician, one of the greatest of all time. The man went blind, and even that didn't slow him down. Euler's productivity is one of the most significant problems for a biographer. How do you do justice to a man who wrote so much and touched so many aspects of mathematics? You can't, sadly. There are biographies out there, but none of them are comprehensive. Furthermore, none of them are in English.
Paul J Najin goes over some applications and miscellaneous curiosities related to Euler's Equation. The book is more advanced than I thought, but that is not a real issue. The book splits into six chapters. It has essays that cover different aspects of the formula. I thought the book was great, but as I said, I couldn't understand some of the main ideas. For your reference, I reached Calculus II in school, but I didn't do well in the class.
Thanks for reading my review, and see you next time.
As you all know, Leonhard Euler was a genius mathematician, one of the greatest of all time. The man went blind, and even that didn't slow him down. Euler's productivity is one of the most significant problems for a biographer. How do you do justice to a man who wrote so much and touched so many aspects of mathematics? You can't, sadly. There are biographies out there, but none of them are comprehensive. Furthermore, none of them are in English.
Paul J Najin goes over some applications and miscellaneous curiosities related to Euler's Equation. The book is more advanced than I thought, but that is not a real issue. The book splits into six chapters. It has essays that cover different aspects of the formula. I thought the book was great, but as I said, I couldn't understand some of the main ideas. For your reference, I reached Calculus II in school, but I didn't do well in the class.
Thanks for reading my review, and see you next time.
January 29, 2021
I thoroughly enjoyed another book of this author called ‘An Imaginary Tale’ and decided to read this follow up book thinking that it would be in the same manner. I was not disappointed. This is an absolutely wonderful and gentle introduction to the Fourier analysis and the signal processing. The author takes extra steps to be clear and approachable with the explanations of the math concepts; pretty much spoon-feeding the reader. A seasoned mathematician might find it annoying, but I think this is a requirement for an introductory text. An small Euler biography at the end of the book was a lovely extra bonus.
January 26, 2018
An excellent book. Well written, without appearing tedious. The author has the gift of presenting advanced mathematics in a very readable format without simplifying it in a childish manner.
Of course, it depends on what you mean advanced. In this case, we are talking about undergraduate level mathematics, which is advanced enough for me at least.
Of course, it depends on what you mean advanced. In this case, we are talking about undergraduate level mathematics, which is advanced enough for me at least.
June 14, 2020
Not for the mathematically faint of heart! Paul Nahin has written a big book about Euler’s equation e^[i*Pi] + 1 = 0 (perhaps the most beautiful equation in history) and its many applications to mathematics, science and engineering. There is also an excellent essay about Euler’s life that alone is worth the price of the book.
August 7, 2018
Very good balance of math details with fun.
December 3, 2013
It's not that engineers shouldn't write books about mathematics, but there should be a disclaimer on the cover, and I should never read them. Actually, in the preface, when the author made a stereotypically engineer-ish remark about the artistic merits of Norman Rockwell over Jackson Pollock, I put the book down and did not pick it up again for months. I should have left it so.
I'm not sure who this book is aimed at, because it sits in an odd place; there's some interesting material in it, but I found it horribly unmotivated for a book that purports to reveal the beauty of Euler's formula, and the level of rigor is low; the focus is more on formulas and workings than principles and proofs, although that isn't to say we don't get a few good ones.
On the plus side, the book is short, especially if you're inclined to skim over the detailed workings.
I'm not sure who this book is aimed at, because it sits in an odd place; there's some interesting material in it, but I found it horribly unmotivated for a book that purports to reveal the beauty of Euler's formula, and the level of rigor is low; the focus is more on formulas and workings than principles and proofs, although that isn't to say we don't get a few good ones.
On the plus side, the book is short, especially if you're inclined to skim over the detailed workings.
July 31, 2022
This book is the companion to author's "The Imaginary Tale" - the story of the long and winding road to the discovery of complex numbers. Whilst the "The Imaginary Tale" has an historical emphasis, "Dr Euler's Fabulous Formula" places emphasis upon the mathematical arguments and explores some of the applications of complex numbers. Some university level mathematics is requried to get the most out of this book.
Want to read
August 31, 2007A 400-page book on "the greatest equation ever," i.e. the so-called Euler's Identity (e^i*pi = 1 = 0). This I must read (or at least try to). Maybe I'll buy it on eBay after I return from my holiday.
August 10, 2014
Hon!, I know little of, and pay no interest to, electrical engineering. Not quite what I was expecting!
January 6, 2015
very technical and you rarely understand the aim...
Displaying 1 - 20 of 20 reviews