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An Imaginary Tale: The Story of √-1 (1998)

por Paul J. Nahin

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897323,730 (3.71)5
Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-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 1878, 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. Some images inside the book are unavailable due to digital copyright restrictions.… (mais)
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Yeah, this one was beyond me. ( )
  jamestomasino | Sep 11, 2021 |
Very technical for a popular book, though admittedly most of my reference points are pop science rather than pop maths. (It's certainly no [b:The Road to Reality: A Complete Guide to the Laws of the Universe|10638|The Road to Reality A Complete Guide to the Laws of the Universe|Roger Penrose|https://images.gr-assets.com/books/1386924912s/10638.jpg|1077395], but it's far more mathematical than any other pop science book I can think of, and it's much more demanding than, say, Ellenberg's excellent [b:How Not to Be Wrong: The Power of Mathematical Thinking|18693884|How Not to Be Wrong The Power of Mathematical Thinking|Jordan Ellenberg|https://images.gr-assets.com/books/1387726285s/18693884.jpg|26542434], which is the only pop maths book I can think of off the top of my head.) In any case, I found it heavy going, and had to accept that a fair portion would go over my head unless I was willing to spend a huge amount of time and effort. So I'm not in a position to judge whether it would be enjoyable for readers with the background & intelligence to follow it closely (though I suspect that it would be).

For me it was worthwhile in parts & frustrating in others. Mostly that's simply the result of my own ignorance/laziness/stupidity, but I did sometimes feel that Nahin wasn't quite sure who he was writing for: he would occasionally pause to explain a very basic concept, then in the next breath launch into a torrent of formal mathematics with little in the way of verbal guidance. (Mostly, though, he was clearly aiming at people with a fairly solid mathematical background.) There were some sections that I could have grasped a lot more quickly & easily with just slightly more hand-holding; sometimes a logical leap that would be obvious to a mathematician took me an embarassingly long time to understand. I assume something similar is true of some of the proofs I gave up on following, though others were genuinely too hard for me, and by the final chapter I was doing a lot of skim-reading.

Anyway, I suspect I might have loved this book had I been a bit smarter or better educated. In reality, it was probably worth reading, but only just. ( )
  matt_ar | Dec 6, 2019 |
On occasion, I find myself in the math/science section of the bookstore. Having a very thorough background in mathematics, I find it interesting to read books written by notable professionals in their fields on certain subjects. This one caught my eye (pun unintended), and I just had to get it!

The book chronicles the history and usage of the imaginary number, i (or j, if you're an electrical engineer), or √-1.

For those of you who have taken a few math classes, you'll realize that i cannot possibly exist in the realm of Real numbers, as with respect to that set of numbers, it simply does not make any sense! Thus, Numbers are broken down into two sets: Real and Imaginary. And when a number contains both of these values, it is considered Complex, or a+bi. Complex numbers work very well as Cartesian coordinates.

But enough about math! Let's discuss Nahin's book. While not having the target audience of The Da Vinci Code in mind, Nahin paints a picture of a 2,000 year old known history of complex numbers, complete with the masterminds who tried to solve problems involving it.

So, if you've ever wondered why we make such a big deal about imaginary number, or how they came to be used in all the different technologies in which they're used, you might find this book interesting. If you think math is boring, but you have an acute case of insomnia, you may also enjoy this book, but for different reasons. The only instance in which I would recommend you avoid this book is if you hate mat and have no intentions of improving your intellect or knowledge of mathematical subjects. ( )
5 vote aethercowboy | Feb 11, 2010 |
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Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-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 1878, 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. Some images inside the book are unavailable due to digital copyright restrictions.

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