Imagining Numbers: (particularly the square root of minus fifteen)How the elusive imaginary number was first imagined, and how to imagine it yourself |
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... the period, rather, stretches over three centuries. And anticipation carries too
progressivist and perhaps too personal a tone, for this “act” doesn't take.
The early mathematicians thought of the square root as a “side”; the sixteenth-
century Italians would at times simply refer to the square root of a number as its
lato, its “side.” Thus, at first glance, negative numbers don't have square roots, for
(as ...
Finally, we will see that our new attitude toward number unifies otherwise
disparate intuitions and helps us interpret an amazing formula that perplexed
sixteenth-century mathematicians. As for prerequisites, the less mathematics you
know, the ...
... you can turn your talents to trying to solve an earlier one, posed in the twelfth-
century text Vija-Gan'ita of Bháskara, Problem 132 (see Colebrooke's Algebra):
The square-root of half the number of a swarm of bees is gone to a shrub of
jasmin ...
Say, lovely woman, the number of bees.23 Ineluctably, however, as the sixteenth-
century Italian mathematicians allowed particular tactics of solution to particular
problems to give way to more general methods applied to more general ...
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LibraryThing Review
Uporabnikova ocena - rcorfield - LibraryThingThis 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 - LibraryThingLiterally 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
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 | |
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Imagining Numbers: (Particularly the Square Root of Minus Fifteen) Barry Mazur Omejen predogled - 2004 |
Imagining Numbers: (particularly the Square Root of Minus Fifteen) Barry Mazur Omejen predogled - 2003 |
Imagining Numbers: (particularly the Square Root of Minus Fifteen) Barry Mazur Omejen predogled - 2004 |