Imagining Numbers: (Particularly the Square Root of Minus Fifteen)

Sprednja platnica
Penguin UK, 25. mar. 2004 - 288 strani
The book shows how the art of mathematical imagining is not as mysterious as it seems. Drawing on a variety of artistic resources the author reveals how anyone can begin to visualize the enigmatic 'imaginary numbers' that first baffled mathematicians in the 16th century.
 

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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

Preface
PART I
Mathematical problems and square roots
What is a mathematical problem?
Square Roots and the Imagination 6 What is a square root? 7 What is a square root?
The quadratic formula
What kind of thing is the square root of a negative number? 10 Girolamo Cardano
Mental tortures
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 45 Many hands
Imagining the dynamics of multiplication by algebra and geometry mixed

Looking at Numbers 12 The problem of describing how we imagine
Noetic imaginary impossible
Seeing and squinting
Double negatives
Are tulips yellow?
Words things pictures
Real numbers and sophists
Forced conventions or definitions?
Charting the plane
The spareness of the inventory of the imagination
The distributive law and its momentum
Bombellis LAlgebra
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
Writing and singing
The power of notation
A plane of numbers
Thinking silently out loud
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
So how can we visualize multiplication in the complex
A few remarks on the literature of discovery and
Understanding Algebra via Geometry
Form and content
The Quadratic Formula
Bibliography
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O avtorju (2004)

Barry Mazur is a celebrated pure mathematician. He is University Professor at Harvard, Harvard's most distinguished faculty post. His work has been influential in many fields and proved vital for the solution of Fermat Last Theorem. Known for the technique called "Mazur's Swindle".

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