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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... Meno's young slave to construct a square whose area is twice the area of a given square. Here is the diagram that Socrates finally draws to help his interlocutor answer the question: The profile of this diagram is a 2 × 2.
... given you the following information about an aquarium tank. The tank holds a volume of 25 cubic feet, and is 1 foot taller than it is wide, and 1 foot longer than it is tall. Find the (precise) dimensions (length, width, height) of the ...
... given that Chuquet was seeking “ordinary number” solutions to his problem. To get a sense, though, of why Chuquet might have been led to think of such expressions—deemed by him impossible—as candidate solutions to the problem, you might ...
... given. “Do you want some more pie?” But we pose (throw out) problems for solution only if we expect that something of a mental stretch is required to come up with the answer. One can classify categories of straightforward question ...
... A/B); to be working in a terrain, an Erewhon, that allows for rational investigation (given its own rules) and reveals its own impossibility. This argument, troubling as it may have been to the early Pythagoreans, has ushered us into 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 |