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Imagining Numbers: (particularly the square…
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Imagining Numbers: (particularly the square root of minus fifteen) (2003)

by Barry Mazur

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This is an interesting little book and I thoroughly enjoyed it.

It sets out to help the user understand and, more importantly, visualise, imaginary numbers (i.e. the square-root of -1). The author tries to use poetic analogies, and historical perspective, as well as a lot of maths, to achieve this.

Mazur does a great job with the maths. The explanations are so clear and the author gently leads the reader forward to interesting insights, and even encourages you to reach for a pen and paper to help with the understanding. He also details the historical story of how the leap was made away from the linear integer line to be able to see how imaginary numbers exist on the complex plane.

For me the poetic analogies were the weakest aspect of this book. They did provide a break and a contrast, but it's the lucidity of the maths and gentle progress towards deeper understanding which makes this a good book. ( )
  rcorfield | Aug 17, 2010 |
I want to read it again. ( )
  spdegabrielle | Dec 10, 2008 |
This book talks about imagination & the history of how complex numbers were imagined & understood by the mathematicians who first came across them. It is readable and well-written. It is maybe a bit repetitive.
  franoscar | Dec 2, 2007 |
Literally a case of "mathematics for poets." The gentlest of intros to imaginary and complex numbers. It certainly doesn't explain things like raising one complex number to the power of another.
  fpagan | Dec 9, 2006 |
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Preface -- 1, 2, 3,... The "counting numbers" are part of us.
[Chapter I -- The Imagination and Square Roots] -- I. Picture this. Picture Rodin's Thinker, crouched in mental effort.
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Amazon.com Product Description (ISBN 0374174695, Hardcover)

How the elusive imaginary number was first imagined, and how to imagine it yourself

Imagining Numbers (particularly the square root of minus fifteen) is Barry Mazur's invitation to those who take delight in the imaginative work of reading poetry, but may have no background in math, to make a leap of the imagination in mathematics. Imaginary numbers entered into mathematics in sixteenth-century Italy and were used with immediate success, but nevertheless presented an intriguing challenge to the imagination. It took more than two hundred years for mathematicians to discover a satisfactory way of "imagining" these numbers.

With discussions about how we comprehend ideas both in poetry and in mathematics, Mazur reviews some of the writings of the earliest explorers of these elusive figures, such as Rafael Bombelli, an engineer who spent most of his life draining the swamps of Tuscany and who in his spare moments composed his great treatise "L'Algebra". Mazur encourages his readers to share the early bafflement of these Renaissance thinkers. Then he shows us, step by step, how to begin imagining, ourselves, imaginary numbers.

(retrieved from Amazon Mon, 30 Sep 2013 13:24:33 -0400)

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