An Imaginary Tale Chapter Summary

Hunter Talley
Mr. Tyc
Pre Calculus
26 Sept. 2014

An Imaginary Tale: The Story of of i [the square root of minus one]

An imaginary tale is the story of the square root of minus one, a number we find described as "impossible" or "imaginary". Nahin's historical and mathematical explanation of complex numbers and functions stretches across two millennia. The square root of minus one was such an unlikely concept for early mathematicians that they ignored it. For centuries mathematicians viewed negative numbers as problematic and were steered clear of difficult expressions such as the square root of a negative number. Publishers describe An Imaginary Tale as a history story, the author describes it as "a book accessible to high school seniors".
A reader with little or no mathematics background could understand the stories of historical famous mathematicians and the story of math growing complete with experiments, discoveries and inventions. To understand this book, a "knowledge of algebra, geometry, trigonometry, calculus and power series.". While this book is easy to understand, a very wide education of mathematics is required to fully understand the illustrations, concepts and mathematical procedures that are challenged to the reader in this book. This book is generally aimed at students that have at least a knowledge of Calculus so they can properly enjoy the book.

The first few chapters are mostly about the history of math, telling us about the great mathematicians: Wallis, Caspar Wessel, Jean-Robert Argand and Gauss. There is plenty of math to work out also. There are many challenging equations and problems in the first few chapters that challenge your mind and its capability. But even more the book covers the equations with complex and imaginary numbers. The real idea of complex numbers is that they can be used for getting results when the use of real numbers impossible. Nahin shows this by using trigonometry, geometry, and basic mathematical functions. Nahin makes it clear that complex numbers allow a shortcut from one real result to another. Nahin tells of the depth of complex numbers and imaginary numbers and how they, combines and separate, can help in the solving and answering of equations and other mathematical procedures. As an engineer, Nahin was always using the square root of minus one as an important and useful number with many practical applications. But An Imaginary Tale is more than a story of usefulness. This accessible and thoroughly researched work lays open the wizardry of complex numbers, exemplifying the pure pleasure of learning what the author himself describes as "pretty mathematics". My favorite part of the book was the beginning of chapter two. Nahin states:
"Despite the success of Bombelli in giving formal meaning to the sqrt of -1 when it appeared in the answers given by Cardan's formula, there still lacked a physical interpretation.
Mathematicians of the sixteenth century were very much tied to the Greek tradition of geometry, and they felt uncomfortable with concepts to which they could not give a geometric meaning. This is why, two century's after Bombelli's Algebra, we find Euler writing in his Algebra of 1770" In the beginning of chapter two, my favorite part, Nahin talks about the "constructions dealing with the square roots of positive lengths". He talks about the impossibility of doing a geometric construction. He says that i was invited to make solving problems easier and more possible. The i takes the place of the square root of -1 when writing out mathematical procedures. My least favorite part was the complex writing of the book. I enjoyed learning about the history of the mathematicians behind the complicated concept of the imaginary number i but the writing was far beyond my comprehension which made it hard for me to understand and pay attention to the book. When I was not able to understand what the book was saying was when I became uninterested and bored with the
book. My overall impression of the book was that it was very interesting. I do not think that I would voluntarily read another book about the history of mathematics because it was not enjoyable in my opinion. The reviews online said that "even though the book was said to be in laymen's terms it was very complex and hard to understand". Most people agree, also, that to understand the story fully, you need at least a college freshman level of calculus which I do not have. In conclusion, learning about the history of mathematics is what this book is about so if you have a strong passion for math then this is a book you should read.