Paperback , pages. Published February 1st by Princeton University Press first published More Details Original Title. An Imaginary Tale: The Story of "i" [the square root of minus one]. Other Editions Friend Reviews. To see what your friends thought of this book, please sign up. To ask other readers questions about An Imaginary Tale , please sign up. Lists with This Book.
Community Reviews. Showing Rating details. More filters. Sort order. Sep 22, WarpDrive rated it it was amazing Shelves: science-and-maths.
And if you persevere, the intellectual rewards to the reader are well worth the effort. The author manages to effectively convey, with concrete and fascinating examples, the intellectual adventure of discovery and unveiling of the beautiful world of complex numbers. Several very intriguing results are demonstrated by the author throughout the book, many of which could not be possibly be demonstrated without the usage of imaginary numbers. The author, in other words, brilliantly and consistently demonstrates what the mathematician Hadamard once said: "The shortest path between two truths in the real domain passes through the complex domain".
The book presents fascinating examples about the physical signature for the complex roots in the plot of quadratic and cubic functions. The relationship between complex numbers and geometry, and physical solutions to real problems, is also treated quite well. The author then effectively demonstrates the sheer beauty and simplicity of the geometric interpretation of the complex numbers and of the corresponding definition of "i" as the rotation operator; he also shows how such interpretation, supported by the famous Le Moivre theorem, can be used to generate countless trig identities.
There is also a quite interesting chapter about the utilization of complex numbers in areas of physics such as special relativity, the derivation of Kepler's first law of elliptical orbit and his other laws from Newton's physics, and in electrical engineering problems. Disappointingly and surprisingly the fundamental character of complex numbers in quantum mechanics is not treated by the author.
I was also disappointed by the fact that fractals are not treated in this book either. In chapter 6 aptly titled "wizard mathematics" , things get mathematically serious: the book gets into more intense but also very intriguing mathematical territory. This is very rewarding albeit somewhat slow read. The Euler's constant and the zeta function are explained in a nice and clear manner. Some of Euler's derivations, so beautifully presented by the author, can be clearly seen as the product of pure, raw genius.
An Imaginary Tale: The Story of √-1 (Princeton Science Library)
And the beauty of higher mathematics can be seen in its power, when we start digging into things such as the derivation of the value of pi from i, the Fresnel integrals, gamma functions extended to complex values and their relationship to the zeta functions, the Riemann hypothesis etc. These are all beautiful derivations and examples almost perfectly executed by the author, with only the very occasional minor typo or missing step or partial demonstration for example, only a trivial case of the reflection formula is actually proved , and occasionally peculiar notational choices.
However it is not a textbook and it does not pretend to be a textbook, so the occasional lack of mathematical rigor is totally forgivable, in my opinion. We finally get, in the last chapter, to the dessert of this rich and rewarding intellectual buffet: complex function theory. I strongly agree with the author when he states: "it wasn't until my first course in complex function theory that I experienced a totally new emotion - the pure pleasure of learning mathematics that was, in and of itself, pretty.
He focuses on Cauchy's first and second integral theorems. The latter theorem is particularly beautiful: the intimate connection between the value of a complex analytical function f z at an internal point inside a region delimited by C, and its contour integral on C, is another illustration of the very special nature of complex functions.
The way the author explain Cauchy's contour integrals is just great. It is clear from the book that the author loves mathematics, appreciates its sheer beauty, and simply loves showing off beautiful equations, graphical tricks, awesome solutions and great intellectual challenges bringing out counter-intuitive and astonishing results. Overall, this is a hugely rewarding book, highly recommended to anybody who loves mathematics. A joy to read. View all 9 comments. Mar 01, Ghada rated it it was amazing Shelves: books , favorites. I've been bored with reading novels lately, so I was looking for something a bit more inspiring and challenging.
This book really hit the spot! I wouldn't call it a non-fiction book per se, but something more of a supplementary book for those interested in digging deeper into a subject. Here the subject under discussion was complex numbers specifically the imaginary number i. In the preface, the author claims that no book has ever been written on this subject alone in a non-text book form, so h I've been bored with reading novels lately, so I was looking for something a bit more inspiring and challenging. In the preface, the author claims that no book has ever been written on this subject alone in a non-text book form, so he took it upon himself to do so he is an electrical engineer and was fascinated with complex numbers while growing up.
Well hats off to Eng. Nahin, because he did an amazing job! The author began with a historical summary of i and the mathematical problems that it surfaced from.
He then moved on to some important applications. I really enjoyed chapters , which contained some problems and uses of complex numbers.uthriretbiosepo.tk
An Imaginary Tale: The Story of the Square Root of Minus One
There was a chapter titled "Wizard Mathematics"!! I had a field day with that one. The title alone was so exciting! I loved going through the proof of how according to complex number theory, the shortest distance between two points is NOT a straight line shortcuts through hyperspace?!? I know right! Even the Appendixes were rich with more problems and proofs, it makes you want to savor every page! I just wish that I had read this book while I was studying complex numbers and Cauchy's Theorems last year.
It would've been easier to work out all the derivations while everything was still fresh. It is definitely worth going through the mathematics yourself using pencil and paper, because let me tell you The Story of i is epic! View 1 comment. Such an elegant way to connect the five most important constants in math, along with fundamental mathematical operations. Unfortunately, the understanding of the math involved in the book, which I'm sure I used to have 50 years ago when I got my BA in math, has left me. I had to skip over most of the equations in the book and there are a lot of them , so I don't even know if I can count this book as "read.
An Imaginary Tale: The Story of ?-1 by Paul J. Nahin, Paperback | Barnes & Noble®
Great history and math book. You definitely need a lot of math to fully appreciate this book if you don't have background up to trig, and preferably calculus, you'll find all but the first couple of chapters impenetrable. If you fit the pre-reqs though, it is very interesting. I found how much my math has degenerated as every now and then I just had to shrug and just move on.
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I do look forward to going back and with pencil and paper trying out some of the more hairy calculations. In An Imaginary Tale , Paul Nahin tells the year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In , when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number.
The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense.
By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits.
This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Paul 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? Many of our ebooks are available through library electronic resources including these platforms:.
Home An Imaginary Tale. His style is far more lively and humane than a mathematics textbook while covering much of the same ground. Readers will end up with a good sense for the mathematics of i and for its applications in physics and engineering. His enthusiasm and informal style easily catch on to the reader. An Imaginary Tale is a must for anyone curious about the evolution of our number concept. Convert currency. Add to Basket. Paperback or Softback.
Condition: New. An Imaginary Tale: The Story of? Seller Inventory BBS More information about this seller Contact this seller. Book Description Princeton University Press, New Book. Shipped from UK. Established seller since Seller Inventory WP Book Description Princeton University Press.
Revised edition. Language: English. Brand new Book. In An Imaginary Tale, Paul Nahin tells the year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i.