Imagining Numbers: (particularly the square root of minus fifteen)Farrar, Straus and Giroux, 1. feb. 2004 - 288 strani How the elusive imaginary number was first imagined, and how to imagine it yourself |
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... objects to be multiplied. Which notation we use reflects where we wish to direct our attention: the equation 2 × 3 = 6 emphasizes the act of multiplying 2 times 3, whereas 2 · 3 = 6 focuses on the result, 6, of that operation ...
... objects. These strange square roots were called imaginary numbers, meaning they were difficult to place among real mathematical objects. And then, an astonishingly satisfying image of these square roots emerged. A way of imagining these ...
... object of the imagination” (at least as a side meaning), is visio, whose standard meaning is “sight.” For a discussion about this (and for a comprehensive history and commentary on what has been said about the imagination), see Eva ...
... objects of the imagination” is a serviceable definition, as far as it goes. It includes things we have seen before but which happen to be absent. Its reach, however, does not encompass the unicorns and sphynxes that tinkers and joiners ...
... objects, that it is only knowable through its objects, that it is remarkable among intentional states for not being easily separable into the double structure of state and object.20 To give a sense of what she means by the.
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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 - 2003 |