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

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Farrar, Straus and Giroux, Feb 1, 2004 - Mathematics - 288 pages
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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.

 

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User Review  - rcorfield - LibraryThing

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 ... Read full review

LibraryThing Review

User Review  - fpagan - LibraryThing

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. Read full review

Contents

Title Page
IMAGINATION
The problem of describing how we imagine
Permission
Charting the plane
The geometry of qualities
The spareness of the inventory of the imagination
JUSTIFYING LAWS
To imagine versus to picture
The inventors of writing
Arithmetic in the realm of imaginary numbers
The absence of time in mathematics
Questioning answers
Back to Bombellis puzzle
Interviewing Bombelli
PUTTING GEOMETRY INTO NUMBERS

Defining the operation of multiplication
The distributive law and its momentum
Virtuous circles versus vicious circles
So why does minus times minus equal plus?
PART II
BOMBELLIS PUZZLE
BombellisLAlgebra 33 I have found another kind of cubic radical
Numbers as algorithms
The name of the unknown
Species and numbers
STRETCHING THE IMAGE
algebra and geometry mixed
Writing and singing
The power of notation
A plane of numbers
NUMBERS
THE LITERATURE OF DISCOVERY
UNDERSTANDING ALGEBRA
THE QUADRATIC FORMULA
BIBLIOGRAPHY
PERMISSIONS ACKNOWLEDGMENTS
Copyright

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About the author (2004)

Barry Mazur does his mathematics at Harvard University and lives in Cambridge, Massachussetts, with the writer Grace Dane Mazur.

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