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

Sprednja platnica
Farrar, Straus and Giroux, 1. feb. 2004 - 288 strani

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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LibraryThing Review

Uporabnikova ocena  - 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 ... Celotno mnenje

LibraryThing Review

Uporabnikova ocena  - 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. Celotno mnenje

Vsebina

Title Page
What is a square root?
NOTES
The problem of describing how we imagine
Permission
Forced conventions or definitions?
What kind of law is the distributive law?
ECONOMY OF EXPRESSION 23 Charting the plane
Back to Bombellis puzzle
Interviewing Bombelli
PUTTING GEOMETRY INTO NUMBERS 45 Many hands
Imagining the dynamics of multiplication by
Writing and singing
The power of notation
A plane of numbers
Thinking silently out loud

The geometry of qualities
The spareness of the inventory of the imagination
JUSTIFYING LAWS 26 Laws and why we believe them
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 31 The argument between Cardano and Tartaglia
Bombellis LAlgebra
I have found another kind of cubic radical which is very different from the others
Numbers as algorithms
The name of the unknown
Species and numbers
STRETCHING THE IMAGE 37 The elasticity of the number line
To imagine versus to picture
The inventors of writing
Arithmetic in the realm of imaginary numbers
The absence of time in mathematics
Questioning answers
The complex plane of numbers
Telling a straight story
SEEING THE GEOMETRY IN THE NUMBERS 53 Critical moments in the story of discovery
What are we doing when we identify one thing with another?
Song and story
Multiplying in the complex plane The geometry
behind multiplication by by 1 + and by 1 +2
What is a number?
So how can we visualize multiplication in the complex plane?
PART III
THE LITERATURE OF DISCOVERY OF GEOMETRY IN NUMBERS 60 These equations are of the same form as the equations for cosines though ...
A few remarks on the literature of discovery and the literature of
UNDERSTANDING ALGEBRA VIA GEOMETRY 62 Twins
Dal Ferros expression as algorithm
Form and content
But
THE QUADRATIC FORMULA
BIBLIOGRAPHY
PERMISSIONS ACKNOWLEDGMENTS
Avtorske pravice

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O avtorju (2004)

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

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